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Data-based Dynamic Modeling for Refinery Optimization

Vahedi, Vahid; Jørgensen, Sten Bay

Publication date:2001

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Citation (APA):Vahedi, V., & Jørgensen, S. B. (2001). Data-based Dynamic Modeling for Refinery Optimization.

https://orbit.dtu.dk/en/publications/a087222d-96bb-4c9a-a43a-a2ee990aad61

Data-based Dynamic Modeling for RefineryOptimization

Ph.D. Thesis

Vahid Vahedi

Center for Computer Aided Process EngineeringCAPEC

Department of Chemical EngineeringTechnical University of Denmark

2800 Lyngby, Denmark

.... and if one does not continue correcting the book for the rest of one's life, it is because the same ironhard discipline, which is required to begin it, is also necessary to complete it.

Gabriel García Márques

Preface

This thesis is written as partial fulfillment of requirements for the Ph.D. degree. The projecthas been carried out as an industrial research project and in collaboration between StatoilRefinery in Denmark and Department of Chemical Engineering at Technical University ofDenmark (DTU). The supervisory group of the project are :

Professor Sten Bay Jørgensen, Center for Computer Aided Process Engineering (CAPEC)Department of Chemical Engineering, DTU,

Senior Engineer, M. Sc. Lars Erik Ebbesen,Statoil Refinery, Denmark

Associated professor Carsten Aamand, IVC-SEP Engineering Research CenterDepartment of Chemical Engineering, DTU,

This project has been carried out as industrial research project, and financed by the DanishAcademy of Technical Science (ATV) and Statoil A/S Denmark.

April 2000

Vahid Vahedi

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Acknowledgments

First of all, I would like to thank professor Sten Bay Jørgensen for his professional guidance,and supervision. I wish to thank the other members of the supervisory group, Senior EngineerLars Erik Ebbesen, and associated professor Carsten Aamand for their guidance, and usefuldiscussions.

A great part of the project was carried out at Statoil Refinery in Kalundborg. Many of theStatoil Refinery employees were involved by their discussions, and guidance. I would like toacknowledge their helpful support.

The last part of the project was carried out during my time at Danisco Sugar and SweetenersDevelopment Center (DSSD). I would like to thanks for their great support andencouragement.

Special thanks goes to the members of Center for Computer Aided Process Engineering(CAPEC). I would like to thank Lars Gregersen for his inspiring ideas and many helpfulcomments along the way, and John Bagtrup Jørgensen for his helpful effort in optimizationsoftware.

I wish to thank all my family and friends for their encouragement. Last but not least, I wish tothank my wife Minoo for her tremendous encouragement, and understanding.

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Summary

This thesis deals with development of data-based dynamic models for refinery processes byusing the methods in Process Chemometrics. The models are developed in order to predict thequalities of intermediate product streams in gasoline processing area. Multivariate predictivemodels are developed for prediction of Research Octane Number (RON), Reid VaporPressure (RVP), and concentration of aromatic compounds, e.g. benzene, in the productstreams of catalytic reformer and isomerization units sent to blendstock tanks which are usedfor gasoline blending.

The chemometric models are applied in a multiperiod nonlinear optimization problem for thegasoline blending in order to provide prediction of previous, present and future values of thequalities in blendstocks tanks based one the variation of the upstream process. Theoptimization goal is to produce the required amount of high quality final gasoline products atthe required time and to minimize the production and inventory costs. Solution of theoptimization problem determines the optimum value of quality and amount of the blendcomponents used in the gasoline blending in such a way that the needed quantities of thedifferent final gasoline products can be produced on-time with the desired specifications withminimum operation and inventory cost.

In this work the available historical data is used to develop models based on information andknowledge obtained from the data. This is data-based modeling and the purpose is to predictquality variables which are expensive or difficult to measure as frequently as it is desired forcontrol and optimization applications.

The general principle for data-based predictive modeling in this work is the methods inProcess Chemometrics. These methods are divided in four general categories according to thelinear, nonlinear, static, and dynamic characteristics of the system under study.A brief review of the methods used in this work for development of data-based dynamic modelis presented. This review include the essence of process chemometrics in order to be able todiscuss the multivariate modeling techniques applied for development of process models in thesubsequent chapters of this thesis. In the class of static linear methods Principal Component Analysis (PCA), PrincipalComponent Regression (PCR), and Partial Least Squares Regression (PLS) are discussed.PCA is used in data assessment, dimensional reduction through extracting the latent variablesand applied mostly for process monitoring. PLS and PCR are used for developinginput-output regression models. In the class of static nonlinear approaches Artificial NeuralNetworks (ANNs) exhibit a strong ability to nonlinear functional approximation. NonlinearPLS regression in which nonlinear function is defined for the inner relationship of the PLS isanother approach in this class of chemometrics methods. A Nonlinear Principal ComponentAnalysis (NLPCA) model is developed based on Input Training Neural Networks (ITNN)which is used for data rectification. The method in the class of dynamic linear includes the methods in System Identification. System Identification deals with knowledge based predictivemodeling using linear time series regression. The linear methods include ARX and ARMAX(Auto Regressive Moving Average with Exogenous input), which are linear models based on

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parametric input output representations. A short description for the dynamic nonlinearmethods is presented, in which the time-series type of model can be integrated in a nonlinearPLS model.

Different criteria in model validation is discussed in which two different reference models asaverage-model and zero-model are presented in order to assess the ability of prediction of thedeveloped chemometric model. The concept of informative data set and persistence ofexcitation is presented, and the issue concerning the impact of closed-loop control onpersistence of excitation of input is discussed

A description of the preliminary steps in the model development work in this thesis ispresented. These preliminary steps concerns mainly with definition of the system limit,description of the output and selected input variables, assessment of data, data scaling andsampling, and description of data treatment. The outliers are found first by visualization ofdata in respective plots, and then a PCA model is performed in order to assess therepresentability of the data, discover any collinearity in the selected inputs, detection ofdistinct clusters of data due to different operation of the plant.

It has been observed that the quality variables are dependent on the previous value ofthemselves and the input variables. This means that a dynamic, time-series modeling approachis a suitable choice in this application. The method applied for model development in this workis ARX (Auto Regressive with Exogenous input) type of model in System Identification, inwhich Partial Least Squares Regression (PLS) method is used for its parameter estimation. The advantage of developing a linear time-series model by a PLS regression is that thevariation and structure of the output variable is directly used in PCA decomposition of theinput variables. Applying PLS will use the strength of PCA in dimensional reduction of thedata set and hence more effective modeling of the output.Since the quality variables are either expensive or time consuming to measure, there are onlya limited number of them available. A solution for the problem of missing output data isproposed by a suitable structure of ARX model.

An optimization model for gasoline processing area of the refinery has been developed. Themodel concerns prediction of the qualities of the products from reforming and isomerizationprocesses and gasoline blending over multiple periods. A decomposition of this model yield in a multi-period optimization model for gasolineblending unit. The objective is to minimize the cost of operation for gasoline production suchthat the quality and quantity demands are satisfied. The optimization model assumes that thequalities of final gasoline product is a linear function of the qualities of the blend componentstreams sent to the blending unit. The objective function is a cost function which represent the cost of operation for productionof gasoline products plus the inventory cost. This objective function is minimized subject to aset of constraints which represent the demands for quality and quantity of final gasolineproducts. The optimum solution yields in quality and quantity of the blend components neededto produced the desired products.A case study is considered and the results are discussed. The results of testing the modelduring the case study indicate that the solution is a feasible, local optimum solution, and thereis good agreement with the demands.

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Resumé

Nærværende afhandling handler om udvikling af data-baserede dynamiske modeller forraffinaderi processer ved anvendelse af metoder i Proces Kemometri. Modellerne er udviklettil forudsigelse af kvalitetsvariable for mellem-produkt strømme i benzin-produktion sektioneni et olie raffinaderi. Multi-variable prædiktive modeller er udviklet til forudsigelse af oktan talResearch Octane Number (RON), damp-trykket Reid Vapor Pressure (RVP), ogkoncentrationen af aromatisk komponenter (benzen) i produkt-strømme fra en katalytiskreformer, og et isomerizerings anlæg. Disse strømme sendes til mellem-produkt tank ogbruges som komponenter i benzin blandingen.

Kemometriske modeller bruges i et multi-periode ikke-lineært optimeringsproblem ibenzin-blandingen til forudsigelse af foregående, nuværende, og fremtidige kvaliteter afindholdet af mellem-produkt tankerne baseret på proces variationen i reformer ogisomerizering anlæg. Formålet med optimeringen er at producere de ønskede mængder af højkvalitets benzinprodukter på en bestemt tid og samtidig minimere produktions og lagringsomkostninger.

Historiske data fra processen udnyttes til at udvikle modeller baseret på informationen gemt idata. Dette kaldes data-baseret modellering og formålet er at forudsige de variabler som erkostbare eller tidskrævende til at måle.

De generelle principper for data-baseret prædiktiv modellering der anvendes i dette projekt ermetoder i Proces Kemometri. Metoderne i proces kemometri er opdelt i fire forskelligekategorier efter lineære og ikke-lineære såvel som statiske og dynamiske egenskaber afsystemet.En kortfattet gennemgang af metoder der anvendes til udvikling af modellerne i dette projekter præsenteret. Denne gennemgang omfatter de væsentlige emner i proces kemometri ogformålet er at kunne diskutere de anvendte fremgangsmåder i modeludviklingen i deefterfølgende kapitler i denne afhandling.Blandt statiske lineære metoder er "Principal Component Analysis (PCA)", "PrincipalComponent Regression (PCR), og "Partial Least Squares Regression (PLS)" diskuteret. PCAbruges til kvalitetsvurdering af data, og dimension reduktion af data og anvendeshovedsageligt til visualisering af processens opførsel. PLS og PCR anvendes til at udvikleinput-output regressions modeller.I den modelklasse der omfatter statiske og ikke-lineære metoder, anvendes "Artificial NeuralNetworks (ANNs)" der omfatter en god evne til approksimation af ikke-lineære funktioner.Ikke-lineær PLS regressions modeller hører også til denne klasse af kemometriske metoder,idet relationen mellem score matricer i input og output er defineret som en ikke-lineærfunktion. En ikke-lineær PCA, "Nonlinear Principal Component Analysis (NLPCA)" model er udvikletbaseret på "Input Training Neural Networks (ITNN)", som kan anvendes til at rektificere data.Metoder i "System Identification" anvendes til dynamiske lineære modeller i proces kemometrisom er specielt egnet til at udvikle prædiktions modeller for dynamiske systemer. SystemIdentifikation omhandler data-baseret prædiktiv modellering ved brug af lineær tids-serie

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regression metoder, såsom ARX og ARMAX (Auto Regressive Moving Average withExogenous input), som er lineær, tids-serie regressions modeller baseret på en parametriskinput-output repræsentation. Dynamiske ikke-lineære metoder er beskrevet kort. Denne typemodel opnås ved at integrere tids-serie modeller i en for eksempel ikke-lineære PLS regressionmodeller.

Forskellige kriterier til model-validering er diskuteret og to reference-modeller er defineret, engennemsnit-model og en nul-model, for at vurdere prædiktionsevnen hos de udvikledekemometriske modeller. Koncepterne i "persistence of excitation" og "informative data" erpræsenteret og virkning af lukket-sløjfe regulering på "persistence of excitation" er diskuteret.

De forskellige trin i udvikling af kemometriske modeller i dette projekt er beskrevet. Dissebestår hovedsagelig af system definition og begrænsning, beskrivelse af input og output data,data skalering, og data behandling. De data som falder langt udenfor normale data områder, desåkaldte outliers, er fundet ved hjælp af først en visualisering af data og dernæst i en PCAanalyse som også bruges til at afsløre lineære sammenhænge mellem input variable, oggrupperinger i data som kan være tegn på forskellige typer af proces operation.

Det er observeret at output variablene er relateret til de tidligere værdier af variablene selv oginput variblene. Dette bevirker at en dynamisk tids-serie modellering kan anvendes.Kemometriske modeller er udviklet ved brug af ARX (Auto Regressive with Exogenous input)i system idenfikation, idet PLS modellen er anvendt til parameter estimationen.Fordelen ved at bruge PLS regressionen i en tids-serie model er at informationen i outputbruges direkte i PCA dekomponering af input variable, samt at PCA modellens evne tildimensionsreduktion bruges hvorved effektiv modellering kan opnås.På grund af at måling af kvalitetsvariablene er både kostbar og tidskrævende er der sparsommemængde af output data til rådighed. En måde at behandle problemet med manglende outputdata er at anvende en passende struktur af ARX modellen.

En optimerings model er udviklet til benzin produktions sektionen på raffinaderiet. Modellendækker produktionen af både blandingskomponenter og de færdige benzinprodukter overmultiple tids-perioder. Dekomponering af denne optimerings model resulterer i en multi-periode optimerings modeltil benzin-blandingen. Formålet er at minimere operationsomkostningerne for benzinproduktionen således at mængde og kvalitets kravene overholdes. I optimerings modellen erdet antaget at selve blandingen er en lineær proces, og kvaliteten i det færdige benzin produkter en lineær funktion af kvaliteten i blandings-komponent strømme som sendes til benzinblander enheden.Mål-funktionen er en "Variable Cost" funktion som repræsenterer processens produktions oglagringsomkostninger. Denne mål-funktion minimeres. Begrænsningerne er specifikationen forproduktet kvalitet og kravet for færdig benzin produktmængde, samt bånd på variablene. Denoptimale løsning indeholder optimale værdier for komponenternes mængde og kvalitet som ernødvendigt for at producere de ønskede produkter. Disse optimale værdier sendes videre tilavancerede proceskontrol for implementering.Et eksempel på en produktion plan er betragtet og resultaterne er diskuteret. Resultaterne fortest af modellen viser at løsningen er en realisabel, lokalt optimal løsning, og der er godeoverensstemmelser med kravet. Modellen svaghed er at priserne for blandings komponenter eruafhængige af proces betingelserne.

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Table of Contents

1 Introduction........................................................................................ 1

1.1 Background ............................................................................................... 1

1.2 Motivation ................................................................................................ 4

1.3 Purpose .................................................................................................... 5

1.4 Method ..................................................................................................... 6

1.5 Outline ....................................................................................................... 8

2 Plant Description................................................................................ 9

2.1 Introduction ............................................................................................... 9

2.1.1 Purpose ............................................................................................. 9

2.1.2 Overview ............................................................................................ 9

2.2 Stabilizer/Spliter ....................................................................................... 11

2.2.1 Deisopentanizer................................................................................. 12

2.3 Catalytic Reformers ................................................................................. 12

2.3.1 Catalytic reformer I ......................................................................... 13

2.3.2 Catalytic Reformer II ....................................................................... 14

2.4 Isomerization Unit .................................................................................. 15

2.4.1 Penex Unit ....................................................................................... 15

2.4.2 Molex Unit ....................................................................................... 16

2.5 Gasoline Blending .................................................................................... 17

2.6 Summary ................................................................................................... 18

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3 Methods in Process Chemometrics .................................................. 19

3.1 Introduction ............................................................................................. 19

3.1.1 Purpose .......................................................................................... 19

3.1.2 Background ..................................................................................... 19

3.1.3 Outline ...... ..................................................................................... 20

3.2 Static Linear Methods ......... ..................................................................... 22

3.2.1 Principal Component Analysis ......................................................... 22

3.2.2 Multivariate Modeling .................................................................... 23

3.2.3 Multi Linear Regression, MLR ......................................................... 24

3.2.4 Principal Component Regression ..................................................... 24

3.2.5 Partial Least Squares Regression ..................................................... 25

3.3 Static Nonlinear Methods .......................................................................... 27

3.3.1 Nonlinear PLS Model ....................................................................... 27

3.3.2 Artificial Neural Networks ................................................................. 27

3.3.2.1 Model Structure and Algorithm ................................................. 27

3.3.2.2 Calibration and Validation ........................................................ 29

3.3.2.3 Example, Prediction of RON for Final Gasoline Product ........... 30

3.3.2.4 Model Structure and Performance ............................................ 31

3.3.2.5 Discussion ................................................................................ 32

3.3.3 Nonlinear Principal Component Analysis ......................................... 33

3.3.3.1 Introduction ........................................................................... 33

3.3.3.2 NLPCA ................................................................................... 33

3.3.3.3 Data Reconciliation ................................................................. 33

3.3.3.4 Combining PCA and NLPCA ................................................... 34

3.3.3.5 Autoassociative Network ......................................................... 34

3.3.3.6 Input Training Neural Network ................................................. 35

3.3.3.7 Combination of Linear PCA and ITNN ..................................... 36

3.3.3.8 Example; Rectification of Splitter Data .................................... 37

3.3.3.8.1 PCA Model ............................................................................. 39

3.3.3.8.2 ITNN Model ............................................................................ 41

3.3.3.8.3 Result ...................................................................................... 41

3.3.3.9 Discussion ............................................................................. 42

3.4 Dynamic, Linear Methods ......................................................................... 43

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3.4.1 Time-series Model ........ ................................................................... 43

3.4.2 Model Structure ............ ................................................................... 43

3.4.3 ARX Model with PLS Regression ...................................................... 45

3.5 Dynamic, Nonlinear Methods .................................................................. 46

3.6 Model Validation Criteria .......................................................................... 46

3.6.1 Definition of Reference Model in Validation .................................. 46

3.7 Persistence of Excitation ......................................................................... 48

3.7.1 Definition of Informative Data Set .................................................. 48

3.7.2 Concept of Persistence of Excitation .................................................. 49

3.7.3 Effect of Closed-loop Control .......................................................... 49

3.8 Summary ................................................................................................. 52

4 Introduction to Model Development ................................................ 53

4.1 Introduction ............................................................................................. 53

4.1.1 Purpose .......................................................................................... 53

4.1.2 Outline ........................................................................................... 53

4.2 Description of Different Steps in Model Development .............................. 55

4.2.1 Model Objective .............................................................................. 55

4.2.2 Selection of Input Variables ............................................................. 55

4.2.3 Data Collection and Sampling ........................................................ 56

4.2.4 Data Treatment ............................................................................... 56

4.2.5 Suitable Modeling Method .............................................................. 57

4.2.6 Calibration; Estimation of Model Parameter ................................... 58

4.2.7 Model Validation ............................................................................ 58

4.3 System Delimitation ................................................................................. 60

4.4 Description of Output Variables ............................................................... 62

4.5 Description of Input Variables .................................................................. 65

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4.5.1 Input Variables for Catalytic Reformer I ........................................ 65

4.5.2 Input Variables for Catalytic Reformer II ........................................ 68

4.5.3 Input Variables for Isomerization Unit .......................................... 71

4.6 Selection of Sample Interval .................................................................... 74

4.6.1 Suitable Sample Frequency ........................................................... 74

4.6.2 Sample Frequency for Input Variable ............................................. 74

4.6.3 Sample Frequency for Output Variable ........................................... 75

4.7 PCA Analysis ............................................................................................ 76

4.7.1 PCA Model for Catalytic Reformer I .............................................. 76

4.7.2 PCA Model for Catalytic Reformer II ............................................. 80

4.7.3 PCA Model for Isomerization Unit ................................................. 84

4.8 Conclusion ............................................................................................... 88

5 Model for Reformate and Isomerate Products .................................. 89

5.1 Introduction ............................................................................................. 89

5.1.1 Purpose .......................................................................................... 89

5.1.2 Background ..................................................................................... 90

5.1.3 Outline ........................................................................................... 91

5.2 Selection of the Method ............................................................................ 92

5.3 Model for Catalytic Reformer I ................................................................. 96

5.3.1 Introduction .................................................................................... 96

5.3.2 RVP Model ..................................................................................... 96

5.3.2.1 Inputs and Output ................................................................... 96

5.3.2.2 Model Structure ................................................................... 97

5.3.2.3 Identification ........................................................................ 97

5.3.2.3.1 ARX Model With All Inputs .............................................. 98

5.3.2.3.2 Reducing the Number of Model Parameters ......................... 105

5.3.2.4 Discussion of Full ARX model Versus Reduced Parameters .. 118

5.3.3 RON Model ................................................................................... 120

5.3.3.1 Inputs and Output ................................................................. 120

5.3.3.2 Model Structure ................................................................... 120

5.3.3.3 Calibration ........................................................................... 121

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5.3.3.4 Validation ............................................................................. 124

5.3.4 Benzene Model .............................................................................. 127

5.3.4.1 Inputs and Output ................................................................. 127

5.3.4.2 Model Structure ................................................................... 127

5.3.4.3 Calibration ........................................................................... 128

5.3.4.4 Validation ............................................................................ 133

5.4 Conclusion ................................................................................................ 136

6 Optimization .................................................................................... 137

6.1 Introduction .............................................................................................. 137

6.2 Optimization Model .................................................................................. 139

6.2.1 Nomenclature ................................................................................. 139

6.2.1.1 Index Sets .............................................................................. 139

6.2.1.2 Variables ............................................................................... 139

6.2.1.3 Parameters ............................................................................ 140

6.2.2 Tank Models .................................................................................. 140

6.2.2.1 Balance Equations ................................................................. 140

6.2.2.2 Well stirred tank assumption .................................................. 141

6.2.3 Mixing Points ................................................................................ 141

6.2.4 Splitting Points .............................................................................. 142

6.2.5 Qualities of Isomerate, and Reformate Streams .............................. 142

6.2.6 Blending Model .............................................................................. 142

6.2.7 Restrictions ................................................................................. 142

6.2.8 Bounds on Variables ..................................................................... 143

6.2.9 Objective Function ......................................................................... 144

6.2.10 Total Optimization Model .............................................................. 145

6.3 Decomposition ......................................................................................... 147

6.3.1 Gasoline Blending ....................................................................... 147

6.3.2 Intermediate Production Planning ................................................ 148

6.3.3 Discussion .................................................................................... 148

6.4 Scheduling ............................................................................................. 149

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6.4.1 Assumptions .................................................................................. 149

6.4.1.1 Term .................................................................................... 149

6.4.1.2 Tank Capacity ........................................................................ 149

6.4.1.3 Gasoline Blending Input and Output Flow Rate ..................... 150

6.4.1.4 Price Index ............................................................................. 151

6.4.2 Gasoline Blending Production Plan ............................................... 151

6.4.3 Results ........................................................................................... 153

6.5 Discussion ................................................................................................ 154

7 Conclusions ................................................................................... 155

7.1 Introduction ........................................................................................... 155

7.2 Modeling .............................................................................................. 156

7.2.1 Conclusion .................................................................................... 156

7.2.2 Future Work .................................................................................. 158

7.3 Optimization ............................................................................................ 159

7.3.1 Conclusion ..................................................................................... 159

7.3.2 Future Work ................................................................................... 160

References ............................................................................................. 161Appendix A ............................................................................................165Appendix B ........................................................................................... 197Appendix C ........................................................................................... 215

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Chapter 1

Introduction

1.1 Background

The control of a typical refinery operation from management down to the smallest process unitcan be hierarchically classified in the following four levels:

1 Planning & Scheduling

2 Optimization

3 Advanced Control

4 Regulation

The highest level is Planning & Scheduling which is responsible for short and long termplanning and scheduling for manufacturing different products in order to fulfill the refinery'sobligation and meet its engagements on time. The lowest level, Regulation, covers theconventional PID controllers used in different unit operations. These two levels, the highestand the lowest, have existed for many years and have continuously been under development.During the last decades Advanced Control has been developed intensively and has caused aremarkable progress in process control engineering.

Chapter 1 Introduction

1

The missing link between the planning & scheduling level and advanced control isOptimization. The optimization system receives goals and constraints from the higher level,which can be for instance the specifications for high quality gasoline. Also, it receivesinformation and constraints from the lower level, for instance the quality of naphtha productsfrom each production unit or capacity of inventory tanks. Based on these information, theoptimization system computes an improved operating point, and the targets for reaching thatpoint. The targets are sent to the advanced control system, that implements the targets bycomputing the appropriate set points for the controllers. Figure 1.1 shows the controlhierarchy along with the different actions at each level. From a topological point of view, theoperations in a refinery are normally divided into the following hierarchical structure, as it isalso shown on the right hand side of figure 1.1:

1 Complete Refinery

2 Processing Area

3 Production Unit

4 Unit Operation

A Processing Area consists of one part of a refinery which has a close economical andfunctional coherence. An example for this is gasoline processing area which consists all thoseunits and sections of the refinery which are directly involved in gasoline production, coveringnaphtha products from crude oil distillation column down to gasoline blending unit and finalproduct tanks. A processing area include several production units

Optimization

Objective Function

Advanced Control

Targets

Data Reconciliation

Constraints

Regulation

Process

Planning & Scheduling

Set Points

To ActuatorsMeasurements

Processing Area

Complete Refinery

Plant

Production Unit

Unit Operation

Figure 1.1: The Control Hierarchy, and Process Plant Hierarchy


2

A Production Unit is a part of processing area in the refinery which is responsible for aspecific product improvement or production of a particular type of product in the processingarea. Examples of production units are catalytic reformer, isomerization unit, anddesulphurization plant. A production unit consists of a sequence of Unit Operations. A unitoperation is the lowest level in the process plant hierarchy for instance a single distillationcolumn.

As it is suggested in figure 1.1, there is direct connections between levels in the control andprocess plant hierarchies. Each of the four levels in the process plant hierarchy determines thefunctional domain and delimitation for the respective level in the control hierarchy. Planning & scheduling at the top of the hierarchy is related to the whole refinery, a processingarea, and even a production unit according to its time horizon. A long-term planning with atime horizon of one or several months is related to the whole refinery. For a specificprocessing area an intermediate-term planning for several weeks of operation is used to checkthe feasibility of the long-term planning. A short-term planning, usually a few days, concernswith a production unit (Singh et. al. 2000, Sullivan 1990, Agrawal 1995). Advanced control isrelated to a production unit in order to control some unit-operations which have closecoherence. The time horizon for advanced control and conventional regulation is normallyhours, minutes, or even seconds for PID controllers. Finally, at the end of the process planthierarchy, a unit operation is subject to the conventional process control.

The long-term planning and scheduling is performed by using an off-line optimization andforecasts for crude oil prices, product demands, and process units performances. Inintermediate-term planning, the information of quantities and qualities of refinery feedstocks,and intermediate products are used to revise and check the feasibility the long-term planning. Optimization is the link needed to close the connection between the short-term planning andcontrol on production unit level in order to produce the required amount of high qualityproducts at the required time and to minimize the production cost.

Gasoline is one of the most important refinery products. The specifications for high qualitygasoline products includes antiknock property, volatility, sulfur and aromatics contents. Theantiknock property is expressed as octane number of the gasoline. The octane number of a fuelis defined as the percentage of iso-octane in a blend with n-heptane that exhibits the sameresistance to knocking as the test fuel under standard condition in a standard engine. Isooctaneand n-heptane are assigned to octane number of 100 and 0 respectively. (Palmer et. al. 1985).There are two standard test procedure in order to characterize the antiknock property. Theseare defined by American Society for Testing and Materials (ASTM). One definition isdesignated by ASTM D-908 and is called Research Octane Number (RON), and the other isMotor Octane Number (MON) under designation ASTM D-357 (Garry et al. 1994). RONrepresents antiknock property under the condition of low speed and frequent acceleration,normally during city driving, and MON represents the engine performance under heavy loadand high speed condition, which is normally the condition of highway driving. The vapor pressure of the gasoline is expressed in Reid Vapor Pressure (RVP) which is givenby ASTM D-323. RVP together with gasoline boiling ranges represent the characteristics ofgasoline like ease of starting, quick warm-up, tendency to vapor lock. High RVP improveengine economics and starting characteristics, and low RVP prevent vapor lock and reduceevaporation losses. The correct RVP is a compromise between high and low vapor pressureand depends very much to ambient temperature, climate, and season of the year and variesbetween 49 kPa in the summer and 93 kPa in the winter (Gary et. al., 1994).


3

The demands for environmental friendly gasoline products includes for instance the limit foraromatic compounds, lead, and sulfur contents in gasoline. A type of hydrocarbon compoundcontaining at least one benzene ring is called aromatic compound. In addition, regulations imposed by the governments in different countries place maximumrestrictions on RVP to limit the emission of volatile organic compound in to the atmosphere.Furthermore, the global efforts for reducing the consumption of fossil oil products,encouragement to use alternative form of energy, and improving the engine efficiency by carmanufacturing company, have caused a downward tendency of gasoline consumption whichconsequently caused an over-capacity situation for the gasoline market.

This situation encourages the refiners to effectively reduce the amount of give-away for theirproducts by employing optimization. The give-away situation can basically occur when severalquality specifications have to be met at the same time and one or two of them become betterthan the desired. Re-blending in the gasoline blending system can also cause a significantreduction in refinery revenue by taking valuable tank space and blending time. Re-blending willbecome necessary if a blend does not meet the specification of the final gasoline product.

1.2 Motivation

The optimization level is an important step in the control hierarchy which is inevitable infulfillment of the following essential requirements:

Maintain product quality

Meet the environmental demands

Reducing the amount of giveaway

Eliminate re-blending

Increasing the profitability and flexibility of the refinery operation is related to produce basicintermediate streams that can be blended to produce a variety of more specified final product.This concept is widely use in gasoline processing area. The gasoline blending challenge is toproduce final gasoline product in such a way as to maximize profit while meeting all thespecifications for the final gasoline products. Optimization of the gasoline blending process isthus an important issue considering that gasoline can yield 60-70% of total revenue of atypical refinery (Singh et al. 2000).

Gasoline blending can be considered as a batch process in which the quality and volume of theproducts are fixed by the refinery production schedule. If the blendstock tanks can beconsidered as so called standing tanks, in which there is no feed to the tank during the periodof blending, then the measured or predicted qualities of the blend components is constantduring the blending and a Linear Programming (LP) approach in optimization of blendingprocess would be successful (Singh et al. 2000). The prediction of the qualities is performedby using multivariate regression methods and then applying a bias updating. The bias updatinginvolves comparing measured blend component qualities with those predicted by the modeland then the difference is added as a constant in order to appropriate the prediction model.The qualities are normally measured by daily laboratory analyses. This approach has been theexisting practice in most refineries in which the quality variation of the blend component isassumed to be unchanged during the period of bias updating.


4

However, the current trend in the process of gasoline blending is based on a continuous feedto the component blend tanks, i.e. so called running tank. In this situation applying thebias-updated regression model would not be adequate since the qualities of the blendcomponent will change due to the upstream process variation. The LP plus bias-updatingformulation will not handle such time-varying feedstock qualities in order to find the optimalsolution for the blending problem. Thus, improved and advanced prediction model is needed for on-line prediction of the qualityin the blendstock tank based on the variation of the upstream process.

The intermediate product used for gasoline blending are the products of different productionunits in the gasoline processing area. The products from catalytic reformer and isomerizationunits are the most important blendstocks. The demand for high octane quality of gasoline has stimulated the use of catalytic reformerand isomerization unit. In the reformer process the hydrocarbon molecule structure is changedto form higher octane aromatics with a minor amount of cracking. In the isomerization processthe isomers are formed from paraffins by catalytic reactions. The qualities for some other blendstocks can be calculated or estimated more easily. Forinstance, oxygenate, butane and isopentane can be assumed to be pure components and thustheir qualities can be reasonably estimated based on pure component property. The qualities ofsome blend components like Light Virgin Naphtha (LVN) can also be calculated or estimatedsince LVN contain light hydrocarbon components which can be identified by chromatographicanalysis. However, for the reformate and isomerate products from catalytic reformers and isomerizationunit it is not possible to estimate or calculate the qualities easily. Besides, the variation of theRVP, and RON qualities, in the product streams of the catalytic reformers and isomerizationunits, i.e. reformate and isomerate, will particularly provide the possibility of producingdifferent gasoline products with more definite octane number and vapor pressurespecifications, and thus larger optimization potential. It is essentially important to haveaccurate information of the RON quality for reformate and isomerate products, since these arethe only high octane number blendstocks applied for gasoline blending. Furthermore, it is expensive to have on-line quality measurements for these intermediateproducts in order to have the same sampling frequency as the other process variables. Theonly existing measurement is laboratory analyses which are available only one per day, i.e. asample rate of 24 hours, for each quality.

Hence, the above mentioned reasons form the foundation of the strong motivation fordeveloping multivariate prediction models for quality variables of the blendstock.

1.3 Purpose

An important basis for optimization of the gasoline blending process is accurate predictivemodels for qualities of the blendstocks, especially reformate and isomerate products fromcatalytic reforming and isomerization processes. The main purpose of this work is to develop data-based dynamic models in order to be able topredict the qualities of the blend components and supply the optimization system by the past,present and predicted future values of the qualities. The developed model are then used in amultiperiod nonlinear optimization problem for the gasoline blending.The models are mainly for prediction of Research Octane Number (RON), Reid VaporPressure (RVP), concentration of aromatic compounds, e.g. benzene, in the blendstocks.


5

The optimization is concentrated around the gasoline blending unit of the refinery, and theobjective is to determine the targets for the advanced control and conventional process controlsystem by minimizing a cost function subject to a set of process and quality constraints in sucha way that the needed quantities of the different final gasoline products can be producedon-time, with the desired specifications. The objective function represent the cost of operationfor production of blending components plus the inventory cost, which is minimized subject toa set of constraints which represent the demands for quality and quantity of final gasolineproducts, provided the prediction of the qualities of the blend components. The methods used in predictive quality modeling and optimization are discussed in the nextsection.

1.4 Method

The new developments in computer technology in general and specifically the developments inchemical engineering sciences made it possible for chemical engineers to handle the problemsconcerning process monitoring, evaluation, modeling, control and optimization moreefficiently. Chemical engineers often need to extract the useful information from a largevolume of data obtained from mostly poorly-known chemical processes. The obtained datafrom a chemical process is often noisy and faulty. Usually, in a control and optimizationapplication, the data must be rectified before it is used in both calibration and validation of theprocess and prediction models. Using first principal methods for prediction of quality variables for oil refinery processes arevery difficult. For example in a catalytic reformer process dehydrogenization, cyclization andisomerization are the desired reactions in which the octane number will be improved (Garry etal. 1994). However hydrocracking and condensation reactions are not desired in this processin which the first one will produce light hydrocarbon and the second one will cause formationof coke. Controlling these reactions and estimating reaction kinetic parameters is a verychallenging job, since the heavy naphtha feed is made up of a complex hydrocarbon mixtureof C7 to C10 . The alternative to first principal models is Data-based Based modeling, in which availablehistorical data is used in order to develop parametric models based on input-output data set.The methods in Process Chemometrics are applied for model development in this work.

Chemometric methods have their background in statistic analysis. Principal ComponentAnalysis (PCA) is used in the data assessment, dimensional reduction, and extracting the latentvariable. Partial Least Squares Regression (PLS), and Principal Component Regression (PCR)are commonly used for developing input-output regression models (Wise 1991, Esbensen etal. 1994, and Wise et al. 1996).Since the qualities of the blendstocks depends on the past values of process variables, adynamic modeling approach is used for model development. In this work most qualityprediction models are developed mainly by ARX (Auto Regressive with Exogenous input)type of models, which are linear models based on time-series parametric input-outputrepresentations. This method has its background in System Identification theory (Ljung,1987). Artificial Neural Network (ANNs) are also used in developing predictive models for the caseof static nonlinear models. ANNs show great ability in nonlinear functional approximation,because of their inherent nonlinarity. A neural network model, applying nonlinear sigmoidtransfer function, can be trained to learn input-output data matching by recursive updating andtraining the internal model parameters, i.e. weights and biases (Haykin, 1994). A multilayer


6

feedforward network can approximate any continuous function with arbitrary accuracy(Hornik, et al., 1989, Cybenko, 1989). Choosing suitable inputs, which are derived from abasic chemical process knowledge is crucial for a successful ANN modeling. In this senseneural networks should not be considered as a black box, and effective implementation alwaysrequires a minimum degree of process knowledge to identify the relevant inputs (R. Braratti,et al., 1995).

Optimization Model

Objective Function

Constraints

Demands

Online Measurement

Data Validation

Optimum Targets to Advanced Cntrol

Quality Prediction Databased Dynamic Model

Figure 1.2: Optimization model, objective function, and constraints

Figure 1.2 shows a schematic diagram of data flow for optimization model; i.e. objectivefunction and constraints. Data from on-line measurement of the variables are available to beapplied in process and quality prediction models after appropriate pre-treatment by removingthe outliers and performing autoscaling. The developed dynamic models are used for prediction of the blend component qualities andused as constrained in optimization model. The blending problem is a multiperiod nonlinearoptimization problem.The demands and specification of final gasoline product are included and expressed as theconstraints. The objective function is a cost function. The optimum values of variables are sentto the advanced control level to be implemented in the control of the gasoline unit.


7

1.5 Outline

In chapter 2 the process plant relevant for this work is described in order to provide a generalknowledge about the mainstream flow and operation of different production units in therefinery. The feed streams to gasoline processing area are three naphtha streams. A set ofstabilizer/splitter followed by catalytic reforming and isomerization processes are the mainproduction units in this processing area that ends with a gasoline blending system and the finalinventory product tanks.

Chapter 3 reviews briefly the methods used in multivariate predictive modeling . This reviewinclude the essence of process chemometrics in order to be able to discuss the multivariatemodeling techniques applied for development of process models in this thesis.

In chapter 4 a description of the preliminary steps in the model development work in thisthesis is presented. These preliminary steps concern mainly with definition of the system limit,description of the output and selected input variables, assessment of data, data scaling andsampling, and description of data treatment. Furthermore, it is attempted to present a scopefor model development and to describe a procedure and different steps in the processchemometric approach of modeling. The described procedure in this chapter can be used asguidelines to model development

In chapter 5 the structure, calibration, validation, and performance of the chemometric modelsdeveloped for prediction of RON, RVP, benzene contents of reformate and isomerateproducts are presented and discussed.

A multi-period optimization model for optimization of gasoline blending is presented chapter6. The optimization model assumes that the prediction models for the streams sent to gasolineblending are available. A case study is considered as a scenario in production planning andscheduling and the optimum solution for this case is discussed.

The conclusions and suggestion for future work for process chemometric modeling andoptimization are presented in chapter 7.


8

Chapter 2

Plant Description

2.1 Introduction

2.1.1 Purpose

The purpose of this chapter is to provide a general knowledge about the mainstream flow andoperation of different production units in the refinery. This description focuses only on themain objective, and function of each production unit. The level of detail in this chapter is basedon confidential consideration. Besides the aim is merely to provide the reader with a processknowledge enough to understand the optimization and quality prediction models discussed inthe following chapters. Hence, the detail in control loop, flow diagram, and operation in someunits are omitted.

2.1.2 Overview

The first major step in refining crude oil is a distillation process to separate the crude oil into3-4 major products. This is a very important process and normally considered as the heart of arefinery. The crude oil distillation column products are, starting from the top of the column,

Chapter 2 Plant Description

9

naphtha, kerosene, Light Gas Oil (LGO), Heavy Gas Oil (HGO), and finally the bottomproduct; fuel oil. The gasoline processing area of the refinery receives three naphtha feed streams and producesthe gasoline products into the final product tanks. The three naphtha feed streams are naphthaproducts of crude oil distillation column, condensate fractionator, and main fractionator invisbreaking/thermal cracking sections. The main production units in this area are three sets ofnaphtha stabilizer/splitter, two catalytic reformer, and one isomerization unit. Light and heavynaphtha, after splitters, are sent through desulfurization and hydro treating processes forremoving sulfur and mercaptanes before sending to the isomerization and two catalyticreformer units. The desulfurization and hydro treating processes are beyond the scope of thiswork, and it is assumed the yield of production is close to 100% in these units.Naphtha consists basically of hydrocarbon molecules from C4 to C10 . Besides, depending ontype of crude oil, a few percent of naphtha contents will be light gas, i.e. butane, propane,ethane, and methane, and also H2S, and mercaptanes; i.e. RSH. (Gary et al, 1994).

HVN

TK-38

ReformateNaphtha

Stabilizer/Splitter

Sec. 600

Catalytic Reformer ISec. 400

TK-09

MTBETK-1320

TK-30/31

TK-40

TK-35

TK-22LVBN

TK-04BF 92

TK-34BF 95

TK-33BF 98

GasolineBlending

C4TK-28/29

ImportBlendstock

TK-06

HVBN

TK-05BF 98

TK-1382TK-1383TK-1375

Export

Isomerization Unit

Sec. 4600 Isomerate

Naphtha from Condensate FractionatorSection 4200

Naphtha HydrofinerSec. 4300

Naphtha fromCrude Oil Distillation Section 200

Deisopentanizer

LVN

LVN

Catalytic Reformer IISec. 4400

IC5

HVN Reformate

NaphthaStabilizer/Splitter Sec 200

NaphthaStabilizer/

SplitterSec.4700

TK-81

Naphtha HydrofinerSec. 300

Naphtha fromFractionatorVisbreaking Section 600

TK-42

TK-23

LVN

Figure 2.1 : A simplified flow diagram of gasoline processing area.

A set of stabilizer/splitter system split the naphtha into a Heavy Virgin Naphtha (HVN) and aLight Virgin Naphtha (LVN). The HVN streams are sent to two catalytic reformers after adesulfurization process, and then the reformate products are sent to tank. LVN is sent first toa deisopentanizer to separate isopentane (IC5 ). The top product of the deisopentanizer is IC5

which is sent to tank to be used as a blend component for gasoline blending. The bottomproduct of the deisopentanizer is partly sent to an inventory tank and used as a blend


10

component and the other part is sent to the isomerization unit, in which the isomerate productfrom this is also accumulated in tank and used as a blend component in gasoline blending.As shown in figure 2.1, the products from isomerization unit; isomerate, catalytic reformerunits; reformate, LVN, and IC5 products, along with butane, purchased oxygenate, purchasedblend stock, are sent to intermediate storage tanks which are later sent through the gasolineblending system, in which the final gasoline product is produced. The LVBN product shown infigure 2.1 is Light Virgin visBroken Naphtha, which is LVN from a visbreaker process.

2.2 Stabilizer/Splitter

As mentioned before, the three naphtha feed streams to the gasoline processing area are sentfrom crude oil distillation column section 200, condensate fractionator section 4200, and mainfractionator in visbreaking/thermal cracking section 600. Condensate is a product from gasrefinery and contain lighter hydrocarbons than crude oil. The visbroken naphtha containsnormally more olefins than the other two.

Overhead Drum

Stabilizer

Overhead Drum

Splitter

LVN

HVN

Off Gas

Liquid Gas

Off Gas

Naphtha

Figure 2.2: Stabilizer/Splitter; Principal sketch.

The general overview of operation in the three stabilizer/splitters are as follows. Figure 2.2shows a principal sketch of this process. The first step is to separate the light gas from naphthaby distillation. The process is called stabilization. Exceeding concentration of light gas, i.e.methane, ethane, and propane in naphtha will cause formation of emulsion in naphtha andgasoline inventory tanks. The aim of stabilization is to remove the light gases and preventformation of emulsion. The top product of the naphtha stabilizer consists mostly of butane andother hydrocarbons lighter than C4. The bottom product of the stabilizer is stabilized naphtha,which consists of a small amount of C4, C5 and mostly higher hydrocarbons up to C10 .Stabilized naphtha is then sent to naphtha splitter distillation column. Hence, the second step isto split the stabilized naphtha into a Heavy Virgin Naphtha (HVN) and a Light Virgin Naphtha


11

(LVN). LVN is the top product of the splitter and contains mostly of hydrocarbon moleculesbetween C5 to C7 . HVN is the bottom product and consists mostly of C7 to C10. The TrueBoiling Point (TBP) of LVN and HVN from a typical crude oil are in the range of 32-88 0Cand 88-194 0C respectively (Gary and Glenn 1994). The stabilizer can be one single column as shown in figure 2.2 or a series of distillationcolumns for removing ethane, propane, and butane which are normally called deethanizer,depropanizer, and debutanizer respectively.The liquid top product of the splitter in crude oil distillation, i.e. LVN from section 200 infigure 2.1, is mixed with naphtha from condensate fractionator and sent first to adesulfurization process, i.e. hydro treating process, for removing H2S and to convert themercaptanes, RSH, to disulfides; RS-SR. Disulfides are insoluble in water and caustic solution.Then, LVN is sent further to the stabilizer/splitter system in section 4700 as shown in figure2.1. The bottom product of the naphtha splitter, HVN, in section 200 is sent partially to tank andlater mixed with HVBN and sent to a naphtha hydro treating process. The sulfur andmercaptanes are removed and olefins are converted to paraffin by this hydro treating. Thedesulfurized naphtha is sent further to catalytic reformer in section 400.The products from the stabilizer/splitter system in visbreaking/thermal cracking; section 600,are LVBN and HVBN, both referring to light and heavy visbroken naphtha respectively.LVBN is sent directly to tank and used as a blend component. HVBN is mixed with HVNfrom section 200, and sent through naphtha hydro treating process to the catalytic reformer insection 400 as mentioned above.The HVN from splitter in section 4700 is sent directly to catalytic reformer in section 4400,respectively. The LVN is then sent to deisopentanizer in section 250 and further toisomerization unit.

2.2.1 Deisopentanizer

In this section isopentan, i.e. IC5 , is separated from LVN. The feed to this section is LVNsupplied by splitter in section 4700. The liquid top product is IC5 and sent to tank as a blendstock for gasoline blending, which contains the maximum possible IC5 and has an octanenumber of approximately 89. A part of the bottom product of deisopentanizer is sent to LVN tank, and the other part is sentto isomerization unit.

2.3 Catalytic Reformers

The purpose of operation in catalytic reformer is to produce high octane number reformatefrom low octane desulfurized HVN and HVBN in order to provide the blend stock forgasoline blending. Hydrogen is produced in this process and later used in hydro treatingprocesses and isomerization unit.Dehydrogenization, cyclization and isomerization are the desired reactions in which the octanenumber will be improved and hydrogen will be produced. However hydrocracking andcondensation reactions are not desired in this process in which the first one will produce lighthydrocarbons and the second will cause coke formation. The catalytic reactions are mainlyendothermic. More detail canbe found in Gary et al, 1994.Generally, the process consists of a heater, a sequence of fixed bed reactors, a gas-liquidseparator and finally a stabilizer distillation column.


12

There are two catalytic reformers in gasoline processing area. We just call them by I and II, orsection 400 and section 4400 respectively. The strucure of the two reformers are principallythe same, and minor details are out of scope of this work. The reformers are described in thefollowing sections.

2.3.1 Catalytic Reformer I

Figure 2.3 shows a schematic diagram of this production unit. The desulfurized HVN feedstream is mixed with a recycle H2 gas stream. Mixing H2 with HVN is mainly for preventingundesired hydrocracking and condensation reactions. The combined gas and liquid stream issent through a heat exchanger system before entering heater.

MCOMP

C-401Stabilizer

Desulphurized HVN from section 300

H-402A

R-401 R-403R-402 R-404

C

B

D-401

E-403

E-401E-402E-410

H2 to hydrofiner sections

K-401

E-405

E-411

E-406

D-402

E-407E-408

Offgas

Liquid Gas

Reformate to tank

Figure 2.3: A simplified flow diagram of catalytic reformer I.

The feed stream enters in coil A of the heater and continue to the first reactor; R-401. Becauseof the endothermic reactions, the outlet stream of the R-401 is sent back to the heater throughcoil B and further to reactor number 2; R-402. Again the output of the R-402 is warmed up inthe heater by coil C and continue to the third reactor R-403. The outlet stream of the R-403 isthen sent to reactor R-404. The product stream of the R-404 is passed through a set of heatexchanger where the heat from the product stream is transferred to the feed stream to the coilA of the heater, and reboiler E-406 of reformate stabilizer distillation column.The product stream is then cooled in cooler and then sent to product separator drum D-401where the gas is separated from the liquid. The gas consists mostly of hydrogen. The liquidfrom the separator drum is sent to reformate stabilizer. The stabilizer column C-401 produces a liquid bottom product, which is reformate, a gas topproduct and a liquid top product. Reformate product is sent to reformate tank.


13

2.3.2 Catalytic Reformer II

Desulfurized naphtha is sent to this section and mixed with recycle H2 and then sent through aseries of heat exchangers before entering the heater H-4401, as shown in figure 2.4. In H-4401, HVN is warmed up first in convection zone and then in coil A from which it is sentto the first reactor R-4401. The outlet of the R-4401 is sent back to the heater through coil Band further to second reactor R-4402, and again product of this sent to heater and then tothird reactor R-4403. This extensive heating is mainly due to the endothermic catalyticreactions and the necessity for heating the streams before entering each reactor.

MCOMP

R-4401 R-4402 R-4403

Naphtha from C-4703E-4401

E-4402

H-4401

E-4711

D-4401

E-4403

DR-4401

E-4409

D-4404

H2 to Isomerization unit

K-4401

H2 to section 4300

Sour water

D-4408

E-4405

E-4406

Sour waterC-4401

From R-4403

To E-4401

E-4404 A

E-4404 BE-4407

D-4410

Reformate to tank

E-4303E-4406E-4705

Sour water

Figure 2.4: A simplified flow diagram of catalytic reformer II.

The product from the last reactor is sent through a series of heat exchangers for heat recoveryand then to gas-liquid separator drum D-4401. The gas from separator drum is sent to a dryerwhere water and H2S is removed from the gas. A part of gas from the dryer is recycled andmixed with the feed. The liquid from the separator D-4401 is sent to reformate stabilizerC-4401. The gas top product of the stabilizer is sent to gas plant and the bottom product, which isreformate product, is sent to tank as a gasoline blend stock.


14

2.4 Isomerization Unit

The purpose of operation in this section is to convert low octane number LVN to high octanenumber by catalytic isomerization process. The reactions in this process are mainlyexothermic. The feed to the isomerization unit is LVN from deisopentanizer. The isomerization unit ismade up of three parts, namely Penex unit where conversion of LVN takes place, Molex unitwhere separation of isomers takes place, and Hot oil system which is responsible for thenecessary energy supply of the whole unit.

2.4.1 Penex Unit

Figure 2.5 shows a simplified schematic diagram of the Penex unit. LVN feed to theisomerization unit is mixed with extract from the Molex unit, described in section 2.4.2, andhydrogen from catalytic reformer II, section 4400. Then the feed is sent for preheating toE-4608 A/B, E-4609 and E-4610 where the feed is warmed up by the reactor product ofR-4601 A, R-4601 B, and the hot oil system respectively.

LVN from Deisopentanizer

Extract from Molex unitHydrogen from Reformers Hot oil from

H-4681

Oil to D-4681

E-4610

R-4601 A R-4601 B

E-4609 E-4608 A/B

C-4601

Stabilizer

E-4612

D-4604

E-4611

E-4605

Caustic Wash

To Molex Unit

Hot Oil System

Figure 2.5 : A simplified flow diagram of Penex unit.

The feed is then sent to reactors R-4601 A/B. The chemical reactions of isomerization processtake place in R-4601 A/B. The reactor product is sent for exchanging the heat with the feed inE-4609 and then back to R-4601 B. The product of the R-4601B is then sent for cooling inE-4608 A/B and further to stabilizer C-4601. In stabilizer C-4601 the light hydrocarbons are removed from LVN as off gas in the top. Thestabilizer overhead gas is cooled in E-4612 and accumulated in drum D-4604. The liquid fromD-4604 is sent back to C-4601 as reflux. LVN is sent to Molex unit from the bottom of thestabilizer.


15

2.4.2 Molex Unit

In this section the branched; i.e. isomers, hydrocarbon molecules are separated from theother. Figure 2.6 shows Molex part of the isomerization unit.

C-4651

Absorbtion

From PenexBottom product

of C-4601

C-4653

Extraction

D-4656

E-4654

E-4656

Hot Oil System

E-4655

C-4652

D-4653

E-4651

E-4653

Hot Oil System

E-4652

Extracte to Penex

D-4654 Butane to sec. 4700

Butane fromsec. 4700

E-4606

Isomerateto tank

Figure 2.6 : A simplified flow diagram of Molex unit.

The bottom product of stabilizer C-4601 in the Penex unit is sent to absorbtion columnC-4651. In this column the separation of isomeric compound takes place by an absorbentmaterial, and butane as a desorbent liquid. The non-chained hydrocarbon molecules is sent from C-4651 to extraction column C-4653where the desorbent is separated. Desorbent is sent from top of the extraction column todesorbent drum D-4654. The bottom product of the extraction column C-4653 is cooled inE-4656 and sent back to Penex unit for isomerization. The isomeric compounds is sent as the bottom product of C-4651 to isomerate columnC-4652. Butane is mixed with the bottom product before entering to C-4652. The top productof C-4652 is sent to overhead drum D-4653 via cooler E-4652. A part of liquid from D-4653is sent back to C-4652 as reflux and the rest is sent to C3/C4 splitter C-4705 in section 4700. Aside stream of C-4652 is sent to desorbent drum D-4654. The desorbent from D-4654 isrecirculated to the absorption column C-4651 via heat exchanger E-4653. The bottom product of C-4652, which is isomerate, is cooled in E-4653 by desorbent fromD-4654 and cooler E-4606. Isomerate is then sent to tank.


16

2.5 Gasoline Blending

The purpose of this operation is simply to produce final gasoline products by mixing the blendcomponents. These blend components are mainly produced in the previous sections ofrefinery. Figure 2.1 includes also the gasoline blending unit.

Blend Component Tank no.

Oxygenate TK-20

Butane TK-28+29

Import Naphtha TK-06

LVN TK-09

IC5 TK-30+31

Isomerate TK-23 + 42

Reformate 4400 TK-81

Reformate 400 TK-35

LVBN TK-22

Table 2.1 : Gasoline Blending Components

Tank no. Final Gasoline Product

TK-04 Danish unleaded octane 92 (BF 92)



TK-82 Swedish unleaded octane 95 (SV 95)

TK-33 Swedish unleaded octane 98 (SV 98)

TK-83 German unleaded octane 91 (TYSK 91)

TK-75 German unleaded octane 95 (TYSK 95)

Table 2.2 : Final Gasoline Products

The blending components are listed in table 2.1. The oxygenate is an additive used forincreasing the octane number, it can be MTBE, i.e. Methyl Tertiary Buthyl Ether, ETBE, i.e.Ethyl Tertiary Buthyl Ether, or ethanol. Import naphtha is also used if the produced blendcomponents do not fulfill the desired specifications. The purpose is to minimize theconsumption of oxygenate and import naphtha, since the price of these two components arehigh.. Table 2.2 shows the final gasoline products. The product qualities are well specified. Althoughthere are several important properties of gasoline, the three significant qualities that have thegreatest effects on engine performance are Reid Vapor Pressure (RVP), boiling range, andantiknock characteristic. Antiknock characteristic is measured and represented by octanenumber. There are two type of octane number; Research Octane Number (RON) and MotorOctane Number (MON) which are described in chapter 1.


17

2.6 Summary

In this chapter a general process knowledge about the mainstream flow and operation ingasoline processing area is presented. The level of detail in process description is chosen basedon confidential agreement. Among the production units in this area, we have focused on the following major units: threesets of naphtha stabilizer/spilltters, two catalytic reformers, one isomerization unit, and finallygasoline blending system. Three naphtha streams are sent to the gasoline processing area.These three naphtha feeds are sent from crude oil distillation, condensate fractionator, andmain fractionator column in visbreaking/thermal cracking section. The naphtha feeds are firstseparated into a Heavy Virgin Naphtha (HVN) and a Light Virgin Naphtha (LVN). The HVNstreams are sent to two catalytic reformers after a desulfurization process. The reformateproducts from catalytic reforming processes are sent to storage tank. LVN is sent first todeisopentanizer to separate isopentane (IC5) and then to isomerization unit. The isomerateproduct is then sent to storage tank. The two reformate, isomerate, LVN, and IC5 productsmention above along with oxygenate, butane, import naphtha, and LVBN make totally nineblend components. The blend components are kept in intermediate storage tanks and used forproducing final gasoline products in gasoline blending section. It is desired to minimize theconsumption of oxygenate and import naphtha and reduce the give-away in final products, i.e.minimize the cost of operation, and meet the demand specifications for final gasoline products.


18

Chapter 3

Methods in ProcessChemometrics

3.1 Introduction

3.1.1 Purpose

The purpose of this chapter is to present a review of methods used in process chemometrics.This review include the essence of process chemometrics in order to be able to discus themultivariate modeling techniques applied for development of process models in this thesis.

3.1.2 Background

The background, and basis principles in this research come from many areas. As far as thescope of this work is allowed, it is attempted to include the theory of multivariate modelingtechniques so that the reader does not need to go to many other references in order tounderstand the development of the models in this work.

Chapter 3 Methods in Process Chemometrics

19

There are different approaches for development of models depending upon the purpose of themodel. This purpose may be prediction of a process or quality variable, description of aphenomenon, or assessment of data obtained from chemical processes for process monitoringpurposes. In this work we focus mostly on predictive modeling. This means that we takeadvantage of available historical data to develop models based on information and knowledgeobtained from the data. This is data-based modeling and the purpose here is to predictprocess or quality variables which are expensive or difficult to measure as frequently as it isdesired for control and optimization applications. It is hardly possible to obtain a complete first principles model covering the reformation andisomerization reactions in the respective units, since there are numerous hydrocarboncomponents in the feed stream to these units and also because of high number of reactionsoccurring in the reactors. However, as a general discipline we consider the first principlemodel as a basis for selecting the relevant inputs for prediction models. It is crucial to selectsuitable input variables which contain major variables affecting the variation of the modeloutput. When suitable input variables are chosen, the next step is to estimate the model parameters,and in this sense estimation of model parameters can be defined as an approximation toinput-output functional relationship, in which the best linear or nonlinear relation betweeninput and output variables are found.The choice of different approaches depends on the modeling objective and degree of nonlinearity. The complex refinery processes we are dealing with in this work are indeed highlynonlinear. However, it is possible to predict a single process or quality variable by making alinear approximation.

The general principle selected for knowledge based predictive modeling in this work is themethods in Process Chemometrics. A definition of Chemometrics is given by Wise et al. 1996as follows: "Chemometrics is the science of relating measurements made on a chemical systemto the state of system via application of mathematical or statistical methods". Hence, the methods are based on data obtained from the system, and the purpose is to developan empirical model for estimation of one or more properties of the system. Process chemometrics includes both linear and nonlinear approaches. Moreover, it isimportant to consider the dynamic characteristics of the system. If the variables change withtime, or their current value depends on the earlier values, then an appropriate dynamic modelshould bed used. Here, the time-series type of model is a good candidate.Based on this consideration, the methods in process chemometrics are divided in four generalcategories according to the linear, nonlinear, static, and dynamic characteristics of the systemunder study.

3.1.3 Outline

In the class of static linear methods Principal Component Analysis (PCA), PrincipalComponent Regression (PCR), and Partial Least Squares Regression (PLS) are discussed inthis chapter. PCA is used in data assessment, dimensional reduction through extracting thelatent variables and applied mostly for process monitoring.. PLS and PCR are used fordeveloping input-output regression models. These are all presented and discussed in section3.2.In the class of static nonlinear approaches Artificial Neural Networks (ANNs) exhibit a strongability to nonlinear functional approximation. Nonlinear PLS regression in which nonlinear


20

function is defined for the inner relationship of the PLS is another approach in this class ofchemometrics methods. A discussion of ANN modeling and nonlinear PLS is presented insection 3.3. Furthermore, in section 3.3 a description of Nonlinear Principal ComponentAnalysis (NLPCA) is presented. A NLPCA model is developed based on Input TrainingNeural Networks (ITNN) which is used for data rectification.Section 3.4 deals with the method in the class of dynamic linear methods. In this section themethods used in System Identification are described System Identification deals withknowledge based predictive modeling using linear time series regression. The linear methodsinclude ARX and ARMAX (Auto Regressive Moving Average with Exogenous input), whichare linear models based on parametric input output representationsIn section 3.5 a short description for the dynamic nonlinear class of methods is presented, inwhich the time-series type of model can be integrated in a nonlinear PLS model. A discussion about different criteria in model validation is presented in section 3.6. Twodifferent reference models as average-model and zero-model are presented in order to assessthe predictability of the developed chemometric model.In section 3.7 the concept of informative data set and persistence of excitation is presented.A summary of the methods discussed in this chapter is given in section 3.8.


21

3.2 Static Linear Methods

3.2.1 Principal Component Analysis

Principal Component Analysis (PCA) is a method used for dimensionality reduction of data inwhich the data is decomposed to detect the underlying multivariate correlation structure whichis also called hidden phenomena. PCA is a linear approach for decomposition of the originaldata into structure and noise parts, as it is expressed in equation (3.1). The original data is usually made up of a set of several observations of variables. Eachobservation is called an object and consists of measurement of all variables at the same time.An object has the dimension of the number of the variables, which makes the superficialdimensionality of the data. Discovering the significant variation in the data is the first andimportant step in approaching an understanding of the process. The intrinsic dimensionality isthe number of independent variables underlying the significant nonrandom variation in thedata. These independent variables, also called Principal Components (PCs) or LatentVariables (LV), describe the properties of the original data by discovering the underlyingcorrelation structure.By using PCA an optimal transformation of the data from the original variable space to aprincipal component space, also called factor space, is made in which the essential informationin the data is preserved. There will be a minimum sum of squares difference between theoriginal data and the reconstructed data in PCA.This method is basically a linear method for reduction of data dimensionality with minimumloss of information. Let X represent a (n x m) data matrix, in which n is the number of theobservations and m is the number of variables. A PCA model is an approximation to the datamatrix X, and can be described by the following model:

X = TPT + E = Structure + Noise (3.1)

where T(n x f) and P(m x f) are Score and Loading matrices respectively, E(n x m) is residualor noise, and f is number of principal components . It is useful to formulate the PC model inequation (3.1) as an outer product of individual PC contributions:

X = t1p1T + t2p2

T + .... + t ip iT + .... + t fp f

T + E (3.2)

where ti is the score vector for PCi , pi is the corresponding loading vector, and f is the numberof PCs, which must be less than or equal to the smallest dimension of X, i.e. .f ≤ min {n, m}The loading matrix is a transformation matrix between the original variable space and the PCspace spanned by the principal components. The columns in P are called loading vectors andare orthonormal in which:

p iTp j = 0 for i ≠ j , pi

Tp j = 1 for i = j

Loading vectors give us information about the relationship between the original variables andthe PCs. The columns in T are called the score vectors for each component and are orthogonalin which:

t iTt j = 0 for i ≠ j


22

The scores are the effect of observations on each PC.The concept of principal components is related to eigenvectors of covariance or correlationmatrix of X. The covariance matrix is defined by the following equation:

cov(X) = XTXn − 1

(3.3)

The loading vectors are eigenvectors of cov(X), in which for each pi

cov(X) p i = λi p i (3.4)

where is the eigenvalue associated with the eigenvectors pi . Thus, in PCA the eigenvectorλi

is called principal component, and the associated eigenvalue is a measure of the capturedvariance for each pair of score and loading vector. In equation 3.3, it is assumed that the data X is adjusted to have a zero mean by subtractingoff the original mean, and hence the data is mean centered. This type of data scaling is used inorder to remove the effect of different dimensions in the data. If the mean centered data isadditionally adjusted to unit variance by dividing each column in data matrix by its standarddeviation, then the data is called Autoscaled. Applying autoscaled data in equation 3.3 willgive the correlation matrix of the original data.

PCA model is based on projection of the original data matrix X on to a number of principalcomponents along the direction of the maximum variance or minimum squared projectiondistance. That means that the first principal component (PC1) lies along the direction of themaximum variance, the second principal component (PC2) lies along the direction of the nextmaximum variance orthogonal to the first PC, and so on.

The maximum number of principal components can be either number of variables or numberobservations; i.e. number of objects, depending on which is the smallest, . The effective fulldimension of the PC space is given by the rank of the X matrix. A full model is the case whennumber of PCs is the maximum, i.e. f = min(m,n). In this case the residual E is equal to zeroand the decomposition of X only change the original coordinate system, i.e. the variable space,to the new coordinate system, i.e. the PC space, which is not optimal for separating processstructure from noise since no separation between the structure and noise part of the data isaccomplished. Thus, number of PC must be chosen for an optimum fit so that TPT contains therelevant structure and then noise is collected in E. By this choice we obtain a principalcomponent model as a transformation in which many original dimensions are transformed intoanother coordinate system with fewer dimensions. The transformation is achieved throughprojection or eigenvector decomposition. PCA model involves only with one set of data. Methods relating two sets of data, input andoutput, i. e. X and Y, are generally called multivariate calibration, multivariate regression, orsimply multivariate modeling.

3.2.2 Multivariate Modeling

Multivariate modeling is to establish or find a model for the connection between input andoutput; X and Y. The output (Y) matrix consists of dependent variables and the input (X)matrix contains the independent variables. The multivariate model is simply the regressionrelationship between the empirical input and output. Development of a model implies


23

establishment or in fact estimating the relationship between X and Y. This process is calledcalibration, training, or model parameter estimation, and the X-Y data used for this purpose iscalled calibration or training data set. Statistically, it means that we estimate the parameters ina regression model. The model is then used on a new set of X data in order for prediction ofunknown Y.

3.2.3 Multi Linear Regression, MLR

Let start with a classical example; Multi Linear Regression MLR. The model is expressedmathematically in equation 3.5. This method combines a set of X or input variables in a linearcombination that correlate closely to the corresponding output or Y values.

y = a1x1 + a2x2 + ....... + anxn + E (3.5)

where a0 , a1 , ......, an are constants, and called model parameters. Y and X are output andinput variables, respectively, and E is the residual or error.Equation 3.3 can be reformulated by defining the vectors Y and X representing the outputsand inputs, and vector B for the model parameters.

Y = X B + E (3.6)

It is now desired to determine the model parameters B so that error E is minimized. Acommon procedure is to use the least squares criteria for minimization of ETE in order to findthe optimum model parameters B. An estimate for B parameters can be found by the followingequation (Esbensen et al. 1994):

B = ( XT X )−1 XT Y (3.7)

As it can be seen estimation of B involves a matrix inversion, ( XTX )-1 . If the X variables areinter correlated; i.e. approximately linearly dependent, matrix inversion in equation (3.7)becomes increasingly difficult and in worst case MLR will not work due to the lineardependency. To avoid this unfortunate numerical instability matrix X must have full rank, andthis means some of the variables which correlate with each other must be omitted, which mayresult in loosing information. Another problem that may cause failure of MLR method is error or existence of high level ofnoise in the X data. The MLR solution is represented by a least square plane optimally fittedto all data and implicitly assumed that the X variable are noisfree. It is assumed that only Yvariables is affected by error and not the X variables.To avoid these two problems Principal Component Regression (PCR) model is a goodcandidate in which bilinear projection methods are employed.

3.2.4 Principal Component Regression

A PCA model relies on the projection of the original data matrix X on to a number of principalcomponents along the direction of the maximum variance in the X matrix. This concept is usedin Principal Component Regression (PCR) in order to remove the effect of linear dependencyand high level of noise in the X data.


24

PCR performs first a principal component decomposition exactly as PCA and then Y variableis regressed onto the decomposed X matrix. The score matrix T is used in PCR model insteadof original X data, which is mathematically expressed as follows:

Y = T B + E .(3.8)

in which number of columns in T is equal to the number of PCs retained by the PCA model.By this choice we will obtain a model which is stable and robust against collinear X data, andif the data are defective or noisy. Furthermore, the concept of score and loading matrices canbe used in order to interpret the result.The resulting vector of regression coefficient B, which relate the scores in X to the output Y,is expressed as the following:

B = ( TT T )−1 TT Y (3.9)

The regression vector can be obtained by multiplying the coefficient B by the loading matrix P.

r = P B (3.10)

The estimate of the Y dependent variables can be obtained by multiplying the X matrix by theregression vector.

Y = X r (3.11)

In calculation of regression coefficient B the inverse of the scores covariance is( TT T )−1

used which is perfectly conditioned since the scores are orthogonal. Despite the positive advantages mentioned above, PCR model is still not an optimal solutionfor multivariate calibration. The reason is that all the variation in X data will not necessarilycreate an optimal model to predict Y. In another word, there may easily be structuredinformation in X that have nothing to do with Y. This problem can be avoided by applyingPartial Least Squares (PLS) model in which the regression is performed in order to relate thevariation of the independent variable directly to the variation of the dependent variables.

3.2.5 Partial Least Squares Regression

In PLS regression the variation and the data structure in the dependent variables Y is directlyused in PCA decomposition of the independent variables X. We may think of PLS as asimultaneous decomposition of X and Y are performed using PCA. By this an optimal regression is achieved with less principal components and more predictionability, that also can handle noise, error, and collinearity in X data. In order to explain how PLS works, it is easier to make a simplification and look at PLS assimply two simultaneous PCA analyses. T and P are score and loading matrices related to Xand U and Q are score and loading matrices related to Y as it is shown in equation 3.12, and3.13. Furthermore, one more loading matrix is calculated for X. This extra loading is called Wloadings or PLS-weights.

X = T PT + E (3.12)


25

Y = U QT + F (3.13)

PLS does not really perform two independently PCA analyses but in reality connect the scoresin PCAX and PCAY models and by this let the structure in output data Y, directly affect thedecomposition procedure in input X. Besides, principal components are not the same as inPCA, and they represent only the correlation between Y and X, and thus reduce the influenceof large X variation which in fact does not correlate with Y. Therefore, they are called PLScomponents rather than PCA components.The relationship between the scores U for to the dependent variables Y and the scores T forthe independent variables X is expressed in equation 3.14, in which h denotes residuals.

U = f(T) + h (3.14)

In linear PLS, it is assumed that the function f is defined by a simple linear equation as follows:

u = b t + h (3.15)

The coefficient b is called the inner relationship, or internal regression coefficient.The PLS algorithm can be sketched briefly in a simplified summary as follows. First a PCAanalysis is performed on Y data, and the score for the first PLS-component U1 is used as thestarting value for T1 in PCAX. So T1 is replaced by U1 in PLS algorithm, and decompositionof X data is then performed. By this the PCA model for X data is affected by the structure inY data. After performing PCA on X data, the calculated loading matrix, P, is saved as Wloading weights, and the score for the first PLS-component T1 in X-space is immediately usedas the starting value for the U1 vector. By this we let the structure in X data also affect thePCA analysis on Y data. This procedure of calculation and substitution of U and T continues,also for other PLS-components, in an iterative manner until the convergence is reached. A setof T, W, U, Q matrices are calculated.The PLS regression results in two loading matrices for X data. They are called loadings P andloading weights W or effective loading. The P loadings are the same as obtained in ordinaryPCA and express the relationships between X data and the scores T. The W loadings expressthe relationship between X and Y data, and the columns in W matrix are in factPLS-components. Both P and W matrices are important and may be used for interpretation ofthe PLS model or inspection of the model ability. In practical application, it is preferable to apply a MLR type of model. In PLS regression, thematrices W, Q, and P are used for calculation of a set parameters which correspond toparameters B in equation 3.6. The estimation of the B parameters is performed by using thefollowing equation.

B = W ( PT W )−1 QT ( 3.16)

PLS can also handle several covarying output variables. Its ability to extract the usefulinformation from collinear, noisy, input data which is relevant for modeling the prediction ofthe output variables makes the PLS a powerful tool for linear regression modeling.


26

3.3 Static Nonlinear Methods

3.3.1 Nonlinear PLS Model

As it is described earlier, in linear PLS the relationship between the scores U for to thedependent variables Y and the scores T for the independent variables X is defined by a simplelinear function. In many application of multivariate calibration the relationship between X andY variables are indeed nonlinear. One method to capture the nonlinear correlation is to definea nonlinear function in equation 3.14 for the relationship between the scores U and T. Thisfunction can be defined as a polynomial of arbitrary order as it expressed in equation 3.17.

U = C0 + C1T + C2T2 + C3T3 + .. + h (3.17)

The other method is to describe this functionality by using Artificial Neural Networks (ANNs)in order to approximate the nonlinear relationship between the scores in X and Y.

3.3.2 Artificial Neural Networks

The excellent ability of Artificial Neural Networks (ANN) to consider nonlinearity infunctional approximation problems makes it to a powerful tool for application in processindustry. This ability of ANNs is due their inherent nonlinearity, as it will be described in thefollowing. A multilayer feedforward neural network can approximate any continuos functionwith arbitrary accuracy (Hornik, et al., 1989, Cybenko, 1989).

3.3.2.1 Model Structure and Algorithm

The internal structure of a feed forward network consists of three major parts, each made upof layer(s) of neurons. Figure 3.1 shows a schematic diagram of internal structure of a typicalneural network. The inputs to ANNs are provided in input layer; i.e. layer number one, whichhas the number of neurons equal to the number of input variables. The same is for the lastlayer; output layer, which also has the same number of neurons as the number of outputvariables. Between these two layers, there is one (or more) layer(s) called hidden layer(s), andcontains the most important part of the model parameters which are developed during thecalibration also called the training of the model. The question is now how many neuronsshould be chosen for the hidden layer in order to obtain a robust model with an acceptablemodel performance.The ability of the neural networks to fit arbitrary nonlinear functions depends on the presenceof a hidden layer with nonlinear nodes (Kramer, 1991). A suitable nonlinear function is thesigmoid, which is a continuous , smooth, and monotonically increasing function of the form:

φ(x) = 11 + e−x (3.18)

φ(x) → 1 for x → + ∞φ(x) → 0 for x → − ∞

(3.19)


27

In the example suggested in figure 3.1, we have an input vector with p variables for p inputs, ahidden layer with s1 neurons, and an output layer consisting of q neurons for q outputvariables. Each input is weighted with an appropriate weight W. The elements in weightmatrix W1 (s1 x p) are the corresponding weight for s1 neurons in the hidden layer and pinput variables. Furthermore B1(s1) is a bias vector for the neurons in the hidden layer, whichhas s1 element for the neurons in the hidden layer. In the same manner, a weight matrix W2 ofsize (q x s1) and a bias vector B2(q) is defined for the output layer. The internal activity level of a neuron is defined by an Activity Function as a dot product ofthe weight matrix and input to each layer. For instance the activity of each neuron in thehidden layer is defined as the following:

v j = Σi=1

m

Wjix i (3.20)

This activity function forms the input to the j'th Sigmoid Transfer Function defined inequation (3.18) to calculate the output of the neuron. The output matrix of hidden layer in thisexample can be expressed as follows:

y1 = φ(W1 • X + B1) (3.21)

In the same manner, the output of the last layer of the network is calculated. The network'soutput is often called the predicted value, which is compared with the measured value and anerror is calculated. The network error is calculated as the difference between predicted andmeasured output.

X1

X2

Xp

∑

∑

∑

ϕ(.)

ϕ(.)

ϕ(.)

B1

∑

∑

∑

B2

ν� (�1� )�

Y(1)

w(1) w(2)

ν� (�2� )�

ϕ(.)

ϕ(.)

ϕ(.)

y1

y2

yq

Y(2)

Hidden Layer Output Layer

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

Figure 3.1 : A typical Structure of Neural Network.

In this example, for simplicity, we assumed that the input X in figure 3.1 is a vector of onlyone measurement for each input variable and also the output Y contains one correspondingoutput measurement, i.e. only one object. Normally, in a supervised learning using BackPropagation learning algorithm (Simon Haykin, 1994) , the network is trained on a batch ofsamples. Thus, the input, output and error E of the network are matrices of n number ofsamples.


28

The Root Mean Sum Square of the Error (RMSSE) is another representation for the error anddefined as the following:

RMSSE =Σi=1

n

Σj=1

q

(y ij − −y ij)2

nq (3.22)

where is the average value for the output. −y

Back Propagation is a learning method in which the internal weights and biases in neuralnetwork is adjusted by minimizing the RMSSE. The error is propagated backward through thenetwork to adjust the weights and biases in order to make the actual response of the networkcloser to desired or the target response.In this work the Levenberg-Marquardt (LM) method is used for minimizing the RMSSE andupdating the internal parameter of the network. This method is an approximation to Newton'smethod based on the following :

∆W = (JTJ + αI)−1JTE (3.23)

where J is the Jacobean matrix of derivatives of each error with respect to each weight, E isthe error matrix, and α is a scalar. For larger α equation (3.23) approximates a gradientdescent approach and for smaller α it approaches the Gauss-Newton method.

3.3.2.2 Calibration and Validation

Training an ANN model is actually updating the internal weights and biases by presenting thetraining input-output data set (i.e. calibration set) to the network, and minimizing the error inthe output. The training set consists of a number of input-output batches, which is introducedto the network repeatedly.Generally, the total number of model parameters, i.e. number of weights and biases, should notexceed the number of input-output data batches. If the number of internal parameters exceedthe number of batches, there will be a possibility of obtaining an over-fitted model in which themodel will show poor prediction ability and the model performance will not be satisfactory. The number of neurons in both input and output layer are fixed upon the number of input andoutput variables respectively. Hence, there is only number of neurons in the hidden layerswhich will eventually determine the total number of model parameters. If there are few input-output data set; i.e. few batches, available, there will be a maximum limitfor the number of neurons which can be chosen for the hidden layer. This will naturally makethe upper limit for the number of neurons in the hidden layer. The lower limit is of course onlyone single neuron. The optimum number of neurons in the hidden layer is determined by usingthe prediction ability of neural model through a validation procedure in which the number ofneurons is determined by minimum prediction error in the validation. Cross validation is used for the test of model performance. A separate set of test (i.e.validation) data is chosen and introduced to the network. The model is simulated by freezingthe last internal parameters and calculation of predicted output and also the predictionvariance is performed.A recursive method can be used in order to determine the number of hidden nodes (i.e.neurons). We start with only one neuron in the hidden layer, train the network by using thetraining data set until the calibration variance ( i.e. RMSSEC) is minimum or as low as


29

possible. Then we simulate the ANN model and perform the validation and calculate theprediction variance (i.e. RMSSEP). This will be continued by choosing 2, 3, and more neuronsand plot RMSSEP versus number of nodes. We expect that RMSSEP decrease as the numberof the neurons increase until a certain optimum number is found. This is displayedschematically in figure 3.2.

RM

SS

E

Number of the Neurons in Hidden Layer

Figure 3.2 : RMSSEP versus number of neurons An example of ANN modeling will be presented in the next subsection. This model is a qualityprediction of final gasoline product after gasoline blending.

3.3.2.3 Example, Prediction of RON for Final Gasoline Product

A series of ANN models are developed for prediction of qualities of final gasoline products.These are prediction of RON, MON, RVP, benzene contents of the gasoline product, andprediction of D100 and D70 distillation points. D100 and D70 are percent gasoline evaporatedat 100 and 70 degree Celsius respectively.In this section we will present only one of them as an example which is prediction of RON forfinal gasoline product. The process in gasoline blending unit is described in chapter two. The general principal inquality calculation of the gasoline product in this unit is a simple linear model based on thequality of the blend component. It is expressed mathematically as the following

Q = Σi=1

n

v i q i (3.24)

where:Q is the quality of the product

n is number of blend components

vi is the volume fraction of each blend component

qi is the corresponding quality of the blend component

With the exception of RON and MON all other qualities are directly calculated using equation(3.24). For calculation of RON and MON a nonlinear model is used since the octane quality


30

of the final product is a nonlinear function of qualities of blend components. Description ofthis nonlinear model is out of the scope of this thesis. The objective of developing a model is to predict RON by applying ANNs techniques to coverthe nonlineararity in the octane blending.

3.3.2.4 Model Structure and performance

The training data set contains data for 245 blends, which covers almost a year. The inputs tothe model are 22 measurements of the flow rate and RON quality for 11 streams of blendcomponents from the inventory tanks. The output is only one which the measured RON forthe final gasoline product. Thus, the structure of ANN model is 1 neuron and 22 neurons inoutput and input layers respectively. The hidden layer consists of only two neurons.It is interesting to compare the obtained ANN model with the calculated output using equation3.24 which is a linear model. Cross validation of the ANN model is performed. Figure 3.3 shows the result for comparisonof measured RON, calculated by equation 3.24, and ANN predicted RON. Table 3.1 showsalso the calculated average, and standard deviation for measured, calculated and, ANNpredicted RON respectively. Furthermore, the prediction error, calculated as the differencebetween the measured and ANN predicted output, is shown in table 3.1. This result shows that the ANN model is able to capture the nonlinear relation in RONprediction, since the variance of the prediction error from the developed ANN model is lowerthan the variance for both measurement and calculated linear model.

0 5 10 15 20 25 30 35 4091

92

93

94

95

96

97

98

99

100Comparison of Measured(o),Calculated(+) and ANN Predicted(*)RON

Sample Number

RO

N

Figure 3.3 : Comparison of measured, calculated and ANN predicted RON

It is noteworthy to mention that the training data set cover production of all types of gasolinequalities from octane number 92 to 98 for the official Danish gasoline products. Hence, thestandard deviation reported in table 3.1 is related to these three gasoline products. Standard


31

deviation for RON measurement at laboratory is 0.6, in which RON is measured by applyingNIR techniques.

Validation

Measured Calculated ANN Predicted Prediction Error

Average 95.15 95.35 95.34 -0.0019

STD 2.06 2.17 1.90 0.0053

Max. 99.10 100.59 98.80 0.0144

Min. 91.10 90.43 91.80 -0.0155

Table 3.1 : Statistical data for measured, calculated and ANN predicted RON

3.3.2.5 Discussion

The described ANN model exhibit a good performance for prediction ability. In this case thesystem is static, in which there are direct, instantaneous, links between input output variables(Ljung, et al, 1994). The data used for the training of the models are not time seriesrepresentation of the process. There is no dynamic behavior; i.e. change in state variables overthe time, in the process . The time lag is a few seconds. These characteristics are important fora successful development of ANNs model as a static nonlinear model.

However, when the variables change with time, the system is dynamic and the described staticANN model will not work. The solution is to use a dynamic time-series model which is thesubject of discussion in the following sections of this chapter.


32

3.3.3 Nonlinear Principal Component Analysis

3.3.3.1 Introduction

A Nonlinear Principal Component Analysis (NLPCA) model is proposed for reconciliation ofdata from a refinery naphtha splitter process. The NLPCA model is based on the well knownmethod of Principal Component Analysis (PCA) used for dimensionality reduction in order todiscover the significant variation in the data.The proposed NLPCA model uses the inherent nonlinearity of Artificial Neural Networks(ANNs). The model is based on Input Training Neural Network (ITNN), in which the inputs istrained and adjusted along with the weight and biases of the network. Only one hidden layer isused in the internal structure of the neural network. When the ITNN model is properly trained,the trained input provides the nonlinear factors, which correspond to the principal componentsin the linear PCA model.Input training network is based on Autoassociative Network, which consists of three hiddenlayers, i.e. a mapping layer, a bottleneck layer, and a demapping layer. Only the demappingpart of the network is used in ITNN modelTo achieve a better performance, the nonlinear PCA model starts from a linear PCA approachfor initialization of the inputs to ITNN. The inputs, weights and biases of the network are thentrained to reproduce the corresponding output pattern, which is the rectified data.

3.3.3.2 NLPCA

Nonlinear Principal Component Analysis (NLPCA) is used to uncover both linear andnonlinear significance variation in the data matrix, when nonlinear correlation exist among thevariables. NLPCA has the same criterion of optimality as PCA, in which the sum of squarederrors between the original variables and the NLPCA prediction is minimized.The NLPCA method uses Artificial Neural Networks (ANNs). The nonlinear featureextraction can be performed by Autoassociative neural networks (Kramer, 1991).Autoassociative neural net is a feed forward network made up of three hidden layers; amapping layer, a bottleneck layer and a demapping layer respectively. The dimensionalityreduction is achieved in the hidden layer number two which has a small number of nodes. Thismethod uses back propagation learning algorithm for training the network to perform identitymapping between the input and the output of the network. Another method of NLPCA is an Input Training Neural Network (ITNN) proposed by Tanand Mavrovouniotis, 1995, in which only the demapping layer of Autoassociative neuralnetwork is used and the inputs are trained along with the network parameters. In a properlytrained ITNN, the input layer provides the nonlinear factors or latent variables obtained fromnonlinear dimensional reduction of the data.

3.3.3.3 Data Reconciliation

Data obtained from measurement of process variables are often noisy. In order to applyprocess measurements in modeling, control and optimization of the process, it is oftennecessary to rectify the data by performing a data reconciliation.Traditional data reconciliation involved with minimization of the errors between the measuredand the predicted variables from a rigorous mathematical model. This is in fact a nonlinear


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optimization problem. Application of rigorous mathematical model is difficult for somechemical processes, especially for refinery processes in which the components and theircompositions in the feed streams are unknown. This is a strong motivation for using a statistical approach or neural network modeling forpoorly unknown and highly nonlinear chemical processes.

3.3.3.4 Combining PCA and NLPCA

The purpose of this work is to use the concept of the NLPCA in order to perform datareconciliation of a refinery naphtha splitter process. A PCA model provides a first linearapproach to determine the latent variables. The results from PCA is used as initialization forITNN as a NLPCA to capture nonlinearity in the data pattern. The ITNN reproduce the inputsto the PCA in its output layer. Only one hidden layer is used in the ITNN model. Using the information from PCA model the optimum number of the latent variables, i.e.number of inputs to ITNN, is determined. A total number of fourteen variables are measured for the naphtha splitter process whichimplicitly represent the total mass and energy balance of the distillation column. An ITNN is trained by back propagation using Levenberg-Marquardt learning method, whichis an approximation to Newton's method.

3.3.3.5 Autoassociative Network

This method is used for identity mapping in which the network's inputs are produced at theoutput layer. The architecture of the neural network is made up of three hidden layers, asshown in figure 3.4. The first hidden layer is called mapping layer. The original data matrix isprojected into the feature space, in which the output of the mapping layer represent thenonlinear principal components and therefore has f sigmoid nodes as the number of nonlinearPC's. These f nodes, containing sigmodal transfer functions, make the hidden layer numbertwo which is called the bottleneck layer. Note that the number of nodes in the bottleneck isless than nodes in the mapping layer as a result of dimension reduction of the data. The thirdhidden layer is the demapping layer which represent the inverse mapping function and producethe reconstructed data in the output layer.

Input Layer Mapping Layer Bottleneck Layer Demapping Layer Output Layer

Autoassociative Network

Figure 3.4 : An Autoassociative Neural Network.


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The basic principal of the autoassociative neural network is analogous to the PCA. Based onequation (3.1) and (3.8) and using PTP = I, the following equation can be written for the scorematrix without loss of generality:

T = X P (3.25)

In the nonlinear case, we are looking for score matrix T as a nonlinear function of the X as thefollowing form:

T = G(X) (3.26)

Cybenko (1989) has shown that a feed forward neural network with one hidden layercontaining sigmodal transfer function can approximate any function with arbitrary accuracy.Hence, the first layer in autoassociative neural network, i. e. the mapping layer, is used forapproximate the G function in equation (3.26).

In analogy to the linear PCA, for the demapping of the data from the factor space, i. e.bottleneck layer, to the variable space the demapping layer of the network is used forapproximation of the following H function:

X = H(T) (3.27)

n which the predicted X, i.e. the reconstructed data is produced in the output layer.

3.3.3.6 Input Training Neural Network

In input training neutral network only the demapping part of the autoassociative network isused. The input to the ITNN is trained by extending the back propagation algorithm to updatethe input as well as the network parameters, i. e. weights and biases. An example of ITNNarchitecture is shown in figure (3.5). Tan and Mavrovouniotis (1995) have shown that training an ITNN with one input node andno hidden layer is equivalent to the linear PCA with one PC. Adding a hidden layer of sigmoidtransfer function can basically capture both the linear and nonlinear variation in the data matrixand store the nonlinear PC's in the input layer.Updating the input matrix is based on the extension of the back propagation learningalgorithm. The steepest descent direction is derived as expressed in the equation (3.28) forminimizing the errors between the network's output and the desired output. Let use the samenomenclature as we used in section 3.3.2, and figure (3.1) for ANN modeling. Furthermore,let the desired output be data matrix Y of n samples and m variables, and the output of thenetwork be Y2. The sum squared of errors is calculated by:

E = Σn

Σm

(Y2 − Y)2 (3.28)

The steepest direction for updating the new inputs X matrix is:

∆X = −∂E∂X = − 2 Σ

m(Y2 − Y) ∂Y2

∂X (3.29)


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In this model, which we have linear nodes in the input and output layers and sigmodal nodes inthe hidden layer, the output of the network Y2 is calculated as the following:

Y2 = φ(W1 ⋅ X + B1) ⋅ W2 + B2 (3.30)

where φ is sigmodal transfer function as defined in equation (3.18). The output from thehidden layer A1 is calculated as follows:

A1 = φ(W1 ⋅ X + B1) (3.31)

The first derivative of a sigmoid function of the form φ [ f(x) ] can be calculated by thefollowing equation :

∂φ[ F(X)]∂X = ∂F(X)

∂X φ[F(X)] {1 − φ[F(X)]} (3.32)

Combining equations (3.29) through (3.32) yields:

∆X = − 2 [W1T ⋅ A1 ⋅ ∗ (1 − A1) ⋅ ∗ (W2T ⋅ e)] (3.33)

where the error e is equal to (Y2 - Y).ITNN shows good ability of data rectification and converges much faster than autoassociativenetworks.

Input Trainig Network

y21

y31

y41

ym1

y22

y32

y42

ym2

y23

y33

y43

ym3

y2n

y3n

y4n

ymn

y11 y12 y13 y1n

x11 x21 x31 xn1

x12 x22 x32 xn2

x1f x2f x3f xnf

Figure 3.5: A typical Structure of Input Training Neural Network.

3.3.3.7 Combination of Linear PCA and ITNN

To obtain better and faster result, linear PCA and NLPCA is combined in one model. The data matrix is first mean centered, i.e. the columns in the original data matrix aresubtracted from their mean values, and then variance scaled, i.e. the columns are divided bytheir standard deviation. The data matrix which is mean centered and scaled to unit variance isalso called autoscaled data.


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The autoscaled data is then used for a PCA model. The number of PCs used in the model isbased on the percentage captured variance by each PC. The score matrix T from the PCA model is used for initialization of the input matrix X to theITNN, as is shown in figure 3.6. Then the network is trained by adjusting the input, weights,and biases of the network.

y21

y31

y41

ym1

y22

y32

y42

ym2

y23

y33

y43

ym3

y2n

y3n

y4n

ymn

y11 y12 y13 y1n

x11 x21 x31 xn1

x12 x22 x32 xn2

x1f x2f x3f xnf

Principal ComponentAnalysis

Score Matrix

Figure 3.6: Combining PCA and ITNN.

Initialize Input, X0 by

T, Scores from PCA

Train ITNN keepingX0 = T

Constant

Train Input, X0 Weights, W

Biases, B

Figure 3.7: The Three steps in combining PCA and ITNN.

Training an ITNN by applying PCA initialization is carried out in three steps. First; the initialinputs is set equal to the score matrix from a PCA model. Second; the ITNN network istrained by freezing the inputs and updating weights and biases. Third; the network is trainedby updating inputs, weights, and biases. This procedure is summarized in figure 3.7.

3.3.3.8 Example; Rectification of Splitter Data

ITNN model is used as a NLPCA method for rectifying data obtained from naphtha splitterdistillation column. The process diagram is shown in figure 3.18. A total number of fourteenvariables are measured around the column. These are listed in Table 3.2. The flow rate of thefeed stream, distillate, and bottom product can be used for a total mass balance. A smallamount of gas will be produced at the top of the column if the light gases are not completelyremoved by stabilizer distillation column before the splitter. There is no measurement for the flow rate of the gas at the top. However, the total massbalance of the column can be approximately estimated by using feed, top product and bottomproduct flow rates.


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Overhead Drum

Stabilizer

Overhead Drum

Splitter

LVN

HVN

Off Gas

Liquid Gas

Off Gas

Naphtha

Figure 3.8: A schematic diagram of stabilizer/spiltter system.

No. Description Tag Unit

1 Top Temperature TT 0C

2 Tray 23 Temperature T23 0C




6 Reflux Temperature RT 0C

7 Reflux Flow Rate RF m3/hr

8 Feed Temperature FT 0C

9 Feed Flow Rate FF m3/hr

10 Top Pressure P Bar

11 Top Product Flow Rate LVN m3/hr

12 Bottom Product Flow Rate HVN m3/hr

13 Reboiler Duty QR MW

14 Naphtha Cut Point CP 0C

Table 3.2: Description of the variables.


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There are five measurements of temperature profile inside the column. Besides, temperature ofthe reflux and the feed streams are measured. These variables along with a calculated reboilerduty, i.e. QR, can represent the energy balance of the column.Hydrocarbon components and the composition of the components in the feed stream areunknown. Generally, naphtha is a hydrocarbon mixture with a true boiling point range ofbetween 30-40 0C to around 150-180 0C. A calculated naphtha cut point variable, which is apressure corrected temperature of the naphtha product inside the atmospheric crudedistillation column, can be used for a rough characterization of the naphtha stream produced inthe column.A set of data containing total number of 573 samples each with 14 measurements, with asampling interval of one hour, is chosen for the NLPCA model of the naphtha splitter process.The data correspond to almost 24 days of operation. Figure 3.9 shows the variables value vs.sample number. It is obvious from the figure that the column was operating under differentoperation conditions during that period of sampling.

3.3.3.8.1 PCA model

Using the information from scores for PC1 and PC2, as shown in figure 3.10, we can detectthree major clusters of data that represent three operation regions. These regions can beexplained by two pseudo steady states, and one transient state, which is the transient frompseudo steady state region number one to the number two.We define a pseudo steady state to be the state of the operation in which the changes in statevariables are in relatively lower frequency. We can recognize two clearly pseudo steady stateregions in the data matrix shown in figure 3.7.We can roughly assume that the data from sample number 50 to 280 cover the pseudo steadystate number one and the data from sample number 360 to 573 cover the pseudo steady statenumber two and the rest belong to the transient region. Hence, we split the data in three partsand focus on pseudo steady states. The first step in NLPCA modeling is initialization of the inputs by a linear PCA, as it is shownin figure 3.7. Choosing the number of factors, or number of PCs is an important issue. Table3.3 shows the percent variance captured by each PC.

0 100 200 300 400 500 6000

20

40

60

80

100

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160

180Original Data

Sample

Var

iabl

e V

alue

s

Figure 3.9: The Original Data


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521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566

567 568 569 570 571 572 573

Scores on PC# 1

Sco

res

on P

C#

2

Scores for PC# 1 versus PC# 2

Figure 3.10: Scores for PC1 vs. PC2.

Percent Variance Captured by PCA Model

Principal Eigenvalue % Variance % VarianceComponent of Captured Captured Number Cov(X) This PC Total

--------- ---------- ---------- ---------- 1 7.36e+000 52.59 52.59 2 3.19e+000 22.76 75.35 3 1.72e+000 12.29 87.64 4 9.01e-001 6.44 94.07 5 5.99e-001 4.28 98.35 6 9.68e-002 0.69 99.04 7 5.26e-002 0.38 99.42 8 3.91e-002 0.28 99.70 9 1.44e-002 0.10 99.80 10 1.10e-002 0.08 99.88 11 8.46e-003 0.06 99.94 12 5.31e-003 0.04 99.98 13 1.95e-003 0.01 99.99 14 9.92e-004 0.01 100.00

Table 3.3: Percent Variance Captured by PCs.

If we choose too many factors we achieve a model close to full model in which the noise andthe structure part are not separated and we have still a significant amount of noise in data.However, if we choose too few factors we lose a part of information, probably both the linearand nonlinear information, left in the noise part.


40

Since we are going to use the scores for initialization of the inputs to the NLPCA model, wechoose five PCs in order to include nonlinear information.

3.3.3.8.2 ITNN Model

One of the important issue in ANN modeling is the internal architecture of the network, i. e.choosing the number of nodes in the hidden layer. The original data set is used to check theperformance of the network for different inputs, i.e. number of factors, which is indeednumber of the nodes in the hidden layer in ITNN. The experiences, so far, has shown that, forthis application, choosing more nodes in the hidden layer will not improve the performance.However, increasing the number of factors can significantly reduce the network error.It is important to remember that the number of the internal parameters of the network, i.e.weights and biases, should be less than number of the samples. Number of the internalparameters NE is defined as follows:

NE = f*S1 + S1*S2 + S1 + S2 = Number of Internal Parameters

where f, S1, S2 are number of nodes in the input, hidden, and output layers respectively.When NE is larger than the number of samples, ANN model may results in an "over-fitted", or"over-parametrized" network, which is poor in generalization characteristic. By using RootMean Sum Squared Error (RMSSE) as defined in equation (3.22), we can compare theperformance of the network for different factors (f) and number of nodes in the hidden layer(S1) as shown in table 3.4. As we expect, the RMSSE decreases, both in linear and nonlinearmodels, for increasing the number of nodes in input and hidden layers.

3.3.3.8.3 Results

As it is shown in table 3.4, a number of 5 principal component is the optimum choice in thisexample. The transient region is omitted from the data, and we focus on the pseudo steady states. Justfor the matter of curiosity we develop model for each pseudo steady states separately, andthen combine these two in one model. Hence, two models are developed for the two pseudosteady states. These are called model no. 1 and model no. 2 respectively. Additionally a thirdmodel is developed by training an ITNN using a training data set which is a combination of thetraining data for model no. 1 and 2. This third model is just called model no. 3.

PCA NLPCA No. of PCf

S1 NE

Training Test Training Test

1.890 0.378 0.378 0.135 2 2 48

0.881 0.330 0.236 0.126 3 3 68

0.776 0.258 0.191 0.094 4 4 90

0.627 0.221 0.167 0.086 5 5 114

0.448 0.185 0.160 0.129 6 6 140

Table 3.4: Comparison of the RMSSE for different number of nodes in hidden layer. The results of the obtained RMSSE for the three models is summarized in table 3.5.


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ModelN0.

PCA NLPCA f S1 NE n

Training Test Training Test

1 0.336 0.109 0.202 0.060 5 5 114 125

2 0.252 0.112 0.130 0.110 5 5 114 141

3 0.420 0.196 0.115 0.083 5 5 114 255

Table 3.5: Comparison of the RMSSE for the pseudo steady state regions.

As shown, RMSSE for model number 3, i.e. the model valid for both pseudo steady stateregions, is less than the others. The results for comparison of the NLPCA and the measured data for all 14 variables areshown in appendix M.

3.3.3.9 Discussion

The essential objective of applying nonlinear PCA is to rectify the data obtained from theprocess which is used in process models and quality prediction models. A linear PCA is used for assessment of the number of nodes in the input layer which is thenumber of factors used in the NLPCA model. Besides, the scores from PCA are used forinitialization of the inputs to NLPCA. The NLPCA model is first trained by keeping the inputsconstant equal to the scores from linear PCA, and then trained further by updating both theinputs and the network's parameters.As it can be seen from the results shown in the appendix, the NLPCA model is able toreconstruct the original data. For individual variables, such as for the top product flow rateLVN, the models show some deviation for the original measured data. Model no. 3 showsgenerally better results, since the training data set cover a larger area and contains differentsteady state operation regions.What is interesting for the future work in this field is to apply NLPCA method to trace thetransient state from the data matrix. For optimization and control objectives, it is important tobe able to automatically detect the transient state operation of the column.


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3.4 Dynamic, Linear Methods

3.4.1 Time-series Model

System identification deals with the problem of building mathematical models of dynamicalsystem based on observed data from the system. The characteristic of the a dynamic system isthat the variables change with time, or current output value depends not only on the currentexternal stimuli but also on their earlier values. Output of dynamical systems whose externalstimuli are not observed are often called time series (Ljung, 1987, and 1994). In this section a description of ARX (Auto Regressive with Exogenous input) method insystem identification. This is basically a linear, time series regression model. The prediction models developed in this work apply ARX model extensively. These modelsare described in chapter in the following chapter of this thesis.

3.4.2 Model Structure

The main concept of the modeling work is to use different methods to develop models basedon input-output mapping of data by fitting the model parameters. Following the terminologyand mathematical formulation presented by Ljung (Ljung, 1987), we are seeking the mappingfrom the data set :

ZN = [u(1), y(1), ....., u(N), y(N)] (3.34)

to the parameter estimate as the following: θN

ZN → θN ∈ DM (3.35)

in which N is a finite number denoting the dimension of data set, and DM is a set of values overwhich θ ranges in a model structure M. A model structure is a parametrized set of modelsdefined in equation 5.9.In a general formulation linear time-invariant models are defined as the following:

y(t) = G(q, θ)u(t) + H(q, θ)e(t) (3.36)

in which the G and H are functions of θ and q is the backward shift operator. Moreover,{e(t)} is a sequence of independent random variables with zero mean values and variance λ.The extent of parameter vector θ ranges over a subset of Rd in which d is the dimension of θ.Hence, the model presented in 3.36 is no longer a model, but a set of models obtained fromdifferent values of θ.Specification of the functions G and H will lead to a particular model. A suitable method is tochoose a structure that permits the specification of G and H in terms of finite number ofnumerical values, for instance rational transfer functions or finite dimensional state-spacedescriptions.Parametrization of G and H functions in terms of linear difference equations will lead to modelstructure like ARX and ARMAX.


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A linear difference equation is a simple description of input-output relationship. The modelexpressed mathematically as the following equations.

y(t) + a1y(t − 1) + .... + anay(t − na) =b1u(t − 1) + .... + bnbu(t − nb) + e(t) + c1e(t − 1) + ... + cnc(t − nc) + D

(3.37)

in which:Y(t) is output measurement at time t,U(t) is input measurement at time t,e(t) vector of white noise sequences,na is number of A parameters,nb is number of B parameters,nc is the number of C parameters,D is constant vector.

The model formulation in 3.37 includes the moving average of white noise. This type of modelis also called equation error model, since the white noise term is directly added in thedifference equation.The adjustable model parameter are :

θ = [a1 a2 ... ana b1 b2 ... bnb c1 c2 ... cnc ] (3.38)

The backward operators are defined as the following:

A(q) = 1 + a1q−1 + ... + anaq−na

B(q) = b1q−1 + ... + bnbq−nb

C(q) = 1 + c1q−1 + ... + cncq−nc

(3.39)

Introducing the backward operator in the model defined in 3.37 will lead to the followingformulation of the model as in 3.40 :

A(q)y(t) = B(q)u(t) + C(q)e(t) (3.40)

Notice that the model in 3.37 correspond to the model defined in 3.36 by the following:

G(q, θ) = B(q)A(q) H(q, θ) = 1

A(q) (3.41)

The ARX model is a special case of ARMAX model in which , when nc = 0. C(q) ≡ 1It can be shown that the predictor for the ARX model can be defined as equation 3.41 (L.Ljung, 1987).

y(t θ) = B(q)u(t) + [1 − A(q)] y(t) (3.42)

Introducing the regression vector as the following :

ϕ(t) = [−y(t − 1) ..... − y(t − na) u(t − 1) ..... u(t − nb)]T (3.43)

Then equation 3.42 can be expressed as a linear regression model:


44

y(t θ) = θT ϕ(t) = ϕT(t) θ (3.44)

At time t we can evaluate how good this prediction is by calculating the prediction error:

ε(t, θ) = y(t) − y(t θ) (3.45)

The model parameters are estimated by solving the following optimization problem:

θN = arg minθ

1N Σ

T=1

N

ε2(t, θ) (3.46)

This optimization problem is then solved by using a Least Squares approach. Hence, a set ofoptimal parameters is determined.

3.4.3 ARX model with PLS Regression

The normal procedure in estimation of parameters in ARX model is based on the least squares(LS) method minimizing the prediction error defined in equation 3.46. Another approach is toapply a PLS in parameter estimation of ARX model in order to take advantage of PLS abilityto extract the useful information from collinear, noisy, input data which is relevant formodeling the output prediction.An approach is to construct the regression vector defined in 3.43 considering number of na,and nb parameters in order to define the problem as a linear regression problem as described inequation 3.44. The regression problem can be then solved by using linear PLS regression. The advantage of this method is that a linear time-series model can be developed by a PLSregression in which the variation and the data structure in the Y variables is directly used inPCA decomposition of the X variables. Furthermore, in practical application in process industry there may be a lot of variables whichmay theoretically related to the output variable but the collected data shows no correlation dueto corrupting influence of noise or effect of feed-back control. Applying PLS will use thestrength of PCA in dimensional reduction of the data set and hence an effective modeling ofoutput.


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3.5 Dynamic, Nonlinear Methods

An approach for modeling a dynamic nonlinear system is based on applying nonlinear methodsin time-series type of models.As described earlier, the concept of ARX type of model can be used to define a linearregression problem as described in equation 3.44 by constructing the regression vector definedin 3.43.A nonlinear PLS model, as described in section 3.3.1, can then be applied in order to estimatethe regression parameters in the nonlinear case. This approach is basically the same as in the case of linear ARXPLS described in section 3.4.3in which the inner relationship in PLS is defined by a nonlinear function.The nonlinear function can a polynomial of arbitrary order as it is expressed in equation 3.17,or alternatively using a neural network model.

3.6 Model Validation Criteria

The purpose of model validation is to test the performance of a developed model in order toassess the level of predictability of the model in the operation region of interest.A common and natural method of validation is to simulate the model, which is developed incalibration, by using a separate data set, and compare the model predicted with the measuredoutput. The sperate data set called test set or validation set. It is very important that the validationdata set is closely comparable to the calibration data set, with respect to sampling time,sampling condition. It is important that the validation data set is representative for the targetpopulation. The only difference between the calibration and validation should be the samplingvariance. This sampling variance will comprise those differences between the two data setsthat can only be explained by the two different samplings of n objects, made under identicalconditions. The idea behind the model validation is to evaluate the prediction strength of themodel on data with different noise than the calibration set.There are certain criteria in the validation to be satisfied. The first criterion is the level ofprediction error in validation data set, as described in the following.

3.6.1 Definition of Reference Model in Validation

One way to evaluate the performance of the model is to compare the model RMSSE definedin equation 3.22 with a reference or a pre-defined criterion. A suitable reference which is normally used in assessment of model validation is the varianceof measured output in validation data set. Comparison of the calculated standard deviation forthe measured output and the RMSSE defined in 3.22 will give a measure of predictability ofthe obtained model. We shall illuminate the concept of this comparison further in thefollowing.If we use the average value of the measured output and draw an average line through all theoutput values, then we will have a model described by 3.47.

y(t) = yAVG + e(t) (3.47)

We shall call this model as the average-model. It is obvious that the purpose of the modelingis to predict the output much better than the described average model, otherwise the average


46

value can be used as an estimate for the future value of the output and development of aprediction model is not necessary.This average reference model is computed by first calculating the average of all N measuredoutput values, and then subtract the average from the output itself to calculate EAVG , as thefollowing:

(EAVG) i = y(t i) − yAVG (3.48)

Then, we compute a RMSS of this error by using equation (3.22), and denote it asRMSEAVG for the average-model described in 3.47. It is clear that the RMSEAVG has thesame property as the standard deviation of the measured output.We expect that the developed prediction model should predict a set of output values for aperiod of time which are closer to the measured output than the average value. In this sensewe say that the developed model should be at least better than the average-model in order toaccepted.

A second reference model can be defined as the following. Let consider a model structure of3.44 in which the number of A-parameter is 1, i.e. na=1. Furthermore, consider that thedeveloped prediction model find a set of B-parameters which are close to zero, and anA-parameter value close to one This is shown in the following equation:

y(t) = y(t − 1) + 0 (3.49)

This means that the new prediction of y is equal to the previous y. In this case we have noeffect of input variables. We shall call this as zero-model.Based on this consideration, we compute a EZERO as the following in a general form:

(EZERO) i = y(t i) − y(t i+1) (3.50)

Hence, a RMSS of EZERO , which is denoted by RMSEZRO will give os a reference inassessment of predictability of the obtained prediction model. Thus, the expectation is that amodel with good performance characteristic should be better than the zero-model, meaningthat the developed model has captured the effect of input variables.


47

3.7 Persistence of Excitation

One of the important issue in dynamic modeling of a physical system concern with thecharacteristics of the observed process data. The choice of input has a very substantialinfluence on how much the obtain data is representative and informative for the task ofdynamic modeling. The input signal contains valuable information about the operating pointand determine which part and mode of the system is excited during the period of modelcalibration. In the following more specific definition of informative data set and concept ofpersistence of excitation is presented.

3.7.1 Definition of Informative Data Set

As described in section 3.4.2, a set of linear time-invariant models can be defined, as expressedin equation 3.51, in order for input-output mapping of a set of data ZN by fitting the modelparameters , in which N is a finite number denoting the dimension of data set.θN

y(t) = G(q, θ)u(t) + H(q, θ)e(t) (3.51)

The functions G and H can be specified by rational transfer functions or finite dimensionalstate-space descriptions. By using linear difference equations, in order to perform aparametrization of the functions G and H, a set of model structure of ARX and ARMAX, as itis discussed earlier in section 3.4.2. Hence, the general formulation defined in 3.51 will lead toa set of model structure M obtained from different values of parameter vector θ. Number ofthe models that can be obtained is thus a subset of N.The purpose of model fitting is thus to find the optimal solution of the optimization problemdefined in 3.46. If the data set Z is capable of distinguishing between these different models in the model setM, then we call the data set to be informative enough with respect to the model set. Theassumptions here are that the data set Z is quasi-stationary and the models are lineartime-invariant.A more mathematical definition of informative data set is given by Ljung (Ljung 1987). Aquasi-stationary data set is informative if the spectrum matrix :

Z(t) = [ u(t) y(t) ]T

is strictly positive definite for all ω. The spectrum matrix is defined as:

Φz(ω) =

Φu(ω) Φuy(ω)Φyu(ω) Φy(ω)

(3.52)

The concept of informative data is closely related to the concept of persistently exiting inputs,described in the following.


48

3.7.2 Concept Persistence of Excitation

One of the important aspect of choosing input variables is the second-order property of u,such as Φu(ω), i.e. the spectrum of the input, and the cross spectrum Φue(ω) between input andthe driving noise.Let assume that the data Z is collected in an open loop experiment. Consider aquasi-stationary input signal u(t), with spectrum Φu(ω), and the following filter:

Mn(q) = m1q−1 + ... + mnq−n (3.53)

The definition of persistence of excitation is based on the following result obtained by Ljung.

Mn(e iω) 2 Φu(ω) ≡ 0 (3.54)

The definition is that the input signal u is said to be persistently exiting of order n if for allfilter Mn(q) the relation 3.54 implies that .Mn(e iω) ≡ 0The direct result of this definition is that if Φu(ω) is different from zero at least n points in theinterval of -π>ω>π, then the input signal u is persistency exciting of order n.Moreover, is the spectrum of the signal :Mn(e iω) 2 Φu(ω)

v(t) = Mn(q)u(t)

Hence, the input u that is persistency exiting of order n can not be filtered to zero by a movingaverage filter. Consequently, there must exist a set of θ parameters that give a set of differentand distinguish models due to informative characteristic of input signal. On this basis we saythe data collected under open-loop control is informative if the input is persistency exciting. It is useful to consider a more general definition as the following:A quasi-stationary input signa u(t), with spectrum Φu(ω) is said to be persistently exciting if :

Φu(ω) ⟩0 for all ω

In the result and the definition above, it is assumed that input signal is collected from anopen-loop experiment. However, closed-loop control is applied widely in the process industry.The impact of closed-loop control on persistence of excitation of input is discussed in thefollowing.

3.7.3 Effect of Closed-loop Control

In practical application of input-output modeling in process industry, the input data is normallycollected under output feedback. The reason for the feedback control configuration is mostlyfor production economy and plant safety. Most often, it is not simply allowed to manipulatethe system in process industry in order to perform a set of experiments to insure aninformative and excited input signal. The information obtain from a process in a closed control can be defective for modeling theoutput even if the input is persistency excited. In order to illuminate this, consider thefollowing example.Let us consider a close-loop control configuration as the example shown in figure 3.11.Assume that we have the following first-order model structure:


49

+++ ProcessController yu

Noise vExtra input w1

Noise w2 or set point w3

Figure 3.11: A typical closed-loop control.

y(t) = ay(t − 1) + bu(t − 1) + e(t) (3.55)

and assume that the controller is a proportional regulator :

u(t) = fy(t) (3.56)

Inserting 3.56 into 3.55 will give:

y(t) = (a + bf) y(t − 1) + e(t) (3.57)

which is the model obtained under feedback.Now, consider the following set of parameters, in which α is an arbitrary scalar:(a, b)

a = a + αf

b = b + α(3.58)

It can be seen that all models that can be obtained by parameters in 3.58 will give the samedescription of the system as the models by parameters (a, b) in the closed-loop control. Thiswill lead us to the conclusion that no matter the value of proportional control f, there is noway to obtain two distinguishable models from these sets of model parameters. Theinformation obtained from this system by applying 3.55 is thus not informative enough.Notice that this result i a valid even for an excited input u, and hence the persistency excitingof input is not a sufficient condition in closed-loop data.Moreover, if we restrict the model 3.55 by letting parameter b to be equal to one, then theinformation generated by 3.55 with b=1 will be informative enough to distinguish differentvalue of a-parameters.

However, there is chance to get informative information from a closed-loop system, if theregulator is noisy, nonlinear, time-varying or complex high-order. If it is allowed, a certaincomplexity can be added to a closed-loop system by adding an extra input as it is shown infigure 3.11. The input is now a sum of the output feedback plus the extra input, as equation3.59.

u(t) = Fi(q)y(t) + Ki(q)w(t), i = 1, 2, ....., r (3.59)


50

where Fi(q) and Ki(q) are linear filters. The impact of these linear filters and the extra input is that any high frequency contribution tothe signal spectrum, that is produced by changing filters F and K, can be neglected. This can be realized as an extra input w1, noise w2 to the regulator, or set point changes w3,as it is shown in figure 3.11.


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3.8 Summary

In this chapter a review of methods used in process chemometrics is presented. It is attemptedto present the essence of process chemometrics in order to provide the theoretical background for the multivariate modeling techniques applied to develop process models in thisthesisBased on the definition of process chemometrics, the methods in model development arebased on data obtained from the system, and the purpose is to develop an empirical model forestimation of one or more properties of the system. Process chemometrics includes both linear and nonlinear approaches, and consider the staticand dynamic characteristics of the system. Based on this consideration, the methods in processchemometrics are divided in four general categories according to the linear, nonlinear, static,and dynamic characteristics of the system under study. In the class of static linear methods Principal Component Analysis (PCA), PrincipalComponent Regression (PCR), and Partial Least Squares Regression (PLS) are discussed.PCA is used in data assessment, dimensional reduction through extracting the latent variablesand applied mostly for process monitoring. PLS and PCR are used for developinginput-output regression models. In the class of static nonlinear approaches Artificial Neural Networks (ANNs) exhibit a strongability to nonlinear functional approximation. Nonlinear PLS regression in which nonlinearfunction is defined for the inner relationship of the PLS is another approach in this class ofchemometrics methods. Furthermore, a description of Nonlinear Principal ComponentAnalysis (NLPCA) is presented. A NLPCA model is developed based on Input TrainingNeural Networks (ITNN) which is used for data rectificationThe methods in the class of dynamic linear methods include knowledge based predictivemodeling using linear time series regression. The linear methods include ARX and ARMAX(Auto Regressive Moving Average with Exogenous input), which are linear models based onparametric input output representationsThe dynamic nonlinear, in which the time-series type of model can be integrated in a nonlinearPLS model, is discussed. Furthermore, ANNs model can be applied for estimation of innerrelationship of an ARXPLS model.A discussion about different criteria in model validation is presented in this chapter, in whichtwo different reference model, i.e. average-model and zero-model, are presented in order toassess the predictability of the developed chemometric modelThe concept of informative data set and persistence of excitation are discussed along with theissue concerning the impact of closed-loop control on persistence of excitation of input.


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Chapter 4

Introduction to ModelDevelopment

4.1 Introduction

4.1.1 Purpose

The purpose of this chapter is to describe the preliminary steps in the model developmentwork in this thesis. This introduction concerns mainly with definition of the system limit,description of the output and selected input variables, assessment of data, data scaling andsampling, and description of data treatment. Furthermore, it is attempted to present a general scope of model development and to describethe general procedure and different steps in the chemometric approach of modeling. Thedescribed procedure in this chapter can be used as guidelines to model development.

4.1.2 Outline

In section 4.2 a general description of model development phases is presented. The review ofthe steps in the development procedure presented in section 4.2 can be used as guidelines forchemometric modeling. A more detailed process description and definition of system

Chapter 4 Introduction to Model Development

53

delimitation is presented in section 4.3. This will introduce a clear view of the influence ofvariables in different production units on the interesting quality variables and allow the readerof this thesis to follow the description of input output variables in the following sections. Insection 4.4 and 4.5 description of output and input variables are presented respectively. Thename and description of the variables will be unique in this thesis. These variables are used inthe developed model described in chapter 5. Section 4.6 deals with selection of suitable sampleinterval in which the problem concerning sample frequency is discussed. In section 4.7 a PCAanalysis is presented for data obtained from catalytic reformer I, catalytic reformer II, andisomerization unit. The conclusion for this chapter is presented in section 4.8


54

4.2 Description of Different Steps in Model Development

Development of multivariate process model applying chemometric approach contains someessential steps that have decisive influence on the general characteristic, reliability, andperformance of the obtained model.In the following it is attempted to introduce the different stages that should be consideredcarefully during the model development.

4.2.1 Model Objective

The first step is to define the objective of modeling. This question is often related to whichvariable or quality need to be predicted and where this prediction is going to be implemented.Prediction modeling is needed when a variable, often a quality variable, is difficult, expensive,or time consuming to measure. It can also be the situation that first principles mathematicalmodel for a complex chemical process is hardly available and hence the historical process datais used in order to develop a model to predict the future value of a variable which is used in acontrol or an optimization application. Determination of the objective of modeling is important because it will determine the demandsfor characteristics and accuracy of the model. For example if the model is going to be appliedin an optimization routine, the linear or nonlinear characteristics of the model will becomeimportant in choosing the optimization algorithm. If the model is going to be applied in acontrol application, the objective is to estimate the transfer function of the system and hencethe stability characteristic of the obtained model will be an important issue.

4.2.2 Selection of Input Variables

In this step, it is desired to explore and determine the suitable input variables for prediction ofone or several output variables. This is an essential step, because the data is the main source ofinformation and a reasonable model performance can be expected only when necessary andsufficient information is provided. Selection of appropriate input variables is then important inorder to obtain a set of data which is informative enough with respect to a model set that canbe determined from the data using appropriate chemometric methods. The concept ofinformative data is related to persistence of excitation which is described in chapter 3.Selection of a set of suitable input variables is in fact identifying which variable combinationaffect the variation of model output. This selection is naturally related to a good knowledgeabout the process, based on, if available, a first principles mathematical model describing thefunctional dependency of the model output to the input variables. A first principles mathematical model is unfortunately not available in the complex refineryprocesses. However, using the basic knowledge in chemical engineering, it is possible toperform a qualitative analysis of the system in order to identify which variables are expected toaffect the variation of the desired output. Furthermore, it is possible that the collected data from a system does not reflect the expectedcorrelation between output signal and one or several input variables. This can be often for thereasons such that data is collected under the effect of feed-back control, the choice ofsampling interval is wrong, the collected input and output data are from different operationpoints, or the data is simply corrupted as a result of sensor fault.A correlation analysis can be helpful to explore the functional dependency of output to inputsignal. Notice that the correlation analysis technique is based on the assumptions that the


55

system is linear time-invariant, the error or noise part of the data is normal distributed, anddata is obtained from an open-loop control. Furthermore, one should be cautious about the multivariable effect on the output signal.Applying a quick linear regression analysis, like MLR, or PCR, can give insight to thefunctional dependency of the variables if the relationship is linear. A possible procedure can beto start with simply all possible measured variables and then gradually exclude those variableswhich shows no correlation to the output.When the appropriate calibration method is selected and the model is calibrated, then thephysical meaning of the sign and magnitude of the obtained model parameters should be inagreement with the expectation and knowledge based on a first principles model or practicalexperiences. The predicted output will be sensitive to an input variable if a small variance isobtained in that particular. Hence, the correct choice of input variables should results in smallvariance for the corresponding parameters in the resulting model.

4.2.3 Data Collection and Sampling

When the input and output variables of the model is determined, the next step is to select asuitable sampling rate. Special attention should be paid in collection of data in order to detecterrors, and measurement fault. It is necessary to know the level of noise and the method usedfor measurement of quality variables in laboratory. Sampling rate is a significant factor which is related to the dynamic characteristic of the systemdefined by its bandwidth. The purpose of selecting a suitable sampling frequency is to insurethat the collected data is informative enough to develop a set of models. In many industrial application the sample time for temperature, pressure, and flow rate arearound a few minutes, or even seconds. However, those variables which are measured inlaboratory, often quality variables, can have a sample time of several hours due to the appliedanalysis methods. Besides, if the input variables are from different production units, and eventually with differentkind of chemical processes, the sample time could be different. For the modeling objective theselected sampling frequency is normally determined by a process with a faster dynamiccharacteristics. It is also important to determine the time delay of the system and especially when the variablesare chosen from different unit operations. An impulse or a step response of the system canprovide information about time delay and time constant of the system, provided an estimate ofthe transfer function of the system available. The data should be representative for the process and cover all the operation regions ofinterest, and thus it is important to carefully select periods of operation in order to include thedesired operation modes and area.

4.2.4 Data Treatment

One of the objectives in this step is to identify the outlier, faulty, and missing data. Existenceof outlier and error in measurement can completely mislead the development of the model.Missing data and error can even stop the training and development procedure in somemodeling algorithm. Most of the outliers can normally be detected just by visualizing the data in appropriate plotsof respective variables. One effective way to detect error, outlier, or any abnormality in data is


56

scaling of the data to have zero mean and unit variance. If there is an abnormality in data itwill be obvious after scaling, and can be visualized in a plot of scaled data. Data scaling is a common procedure in chemometric modeling prior to any analysis. There aretwo type of scaling the data. If the data is adjusted to have a zero mean by subtracting off theoriginal mean, then the data is called to be mean centered. This technique is useful in order toremove the effect of different dimensions in data. Autoscaling is called to the second type ofdata scaling and that is when the mean centered data is additionally adjusted to unit variance.In calculation of the covariance matrix of the data in different chemometric method it isassumed that the data is mean centered. If an autoscaled data is applied then the calculatedcovariance matrix will give the correlation matrix of the data. Unless other mentioned, the autoscaled data is used in the modeling work in this thesis

A PCA model can also be applied in order to uncover the abnormality in data. PCA is aneffective tool used for assessment of representability of data, existence of clustering andoutliers. Another problem in data is related to the missing data and when there are periodically lack ofmeasurement in the data set. The missing process data can be due to operation shutdown orproblem in data acquisition system. Regarding the quality variables measured at laboratory, itis simply not possible to have measurement value as quick as the process variables and hencethere will be lack of data for quality variables.

4.2.5 Suitable Modeling Method

The selection of suitable method is highly dependent on nonlinear and dynamic characteristicof the system under study. If there is no time dependency in relationship between output andinput a static model can be a relevant choice, and further if the relationship is linear a MLR orPLS model can be applied for model development. For the case of nonlinear static relationshipa ANNs model can be used to cover the nonlinearity of the system, since neural networksshow great ability of nonlinear functional approximation. The characteristic of the a dynamical system is that the variables change with time, or currentoutput value depends not only on the current external stimuli but also on their earlier values.In this case an ARX type of model in System Identification can be applied which is basically alinear, time-series regression method. The input-output relationship in ARX model isdescribed by a simple linear difference equation. Estimation of parameters in ARX model isbased on the least squares (LS) method minimizing the prediction error. Another approach isto apply a PLS in parameter estimation of ARX model in order to take advantage of PLSability to extract the useful information from collinear, noisy, input data which is relevant formodeling the output prediction.When a dynamic system is also nonlinear, a nonlinear time-series method should be chosen. Ina linear PLS it is assumed that the scores in output block is a linear function of the scores ininputs. A nonlinear PLS approach is based on describing the relationship between scores ininput and output blocks by nonlinear functions like higher order polynomial or neuralnetworks. Hence, for dynamic nonlinear input-output mapping a time-series ARX modelstructure can be applied in which nonlinear PLS approaches is chosen for its parameterestimation.

Most of the complex refinery processes are in fact nonlinear system. However, the purpose ofthis work is not to develop dynamic simulation models. It is desired to model the relationship


57

between the output quality variable and a set of input process variables in a MISO model forsteady state operation. When a steady state operation is considered and the transient regionswhich may exist in shutdown and start-up situations are avoided, a linear time-series modelcan be chosen in order to obtain a linear approximation of the relationship between outputquality and input process variables. Regarding the choice of nonlinear models, special attention may be paid to the fact thatselection of nonlinear approaches in quality modeling may result in a more complexoptimization problem, which may cause complications in solving the problem. We may startwith a linear approach, like ARX or PLS, and analysis the performance of the model and resultof the validation, and then decide whether it is necessary to continue with nonlinearapproaches.

4.2.6 Calibration; Estimation of Model parameter

The calibration, also called training, of the model is the main part of model development andthe purpose is to estimate the model parameters, in which certain a criterion is satisfied. Thiscriterion is basically the level of prediction error in training data set. In most of the processchemometrics methods estimation of the model parameters are based on an optimum solutionfor an optimization problem in which sum of squared prediction errors is minimized. The resultis a set of optimum value for the model parameters. The obtained model is then applied invalidation in order to assess the predictability and general characteristic of the model. In thissense, although the calibration and validation are two separate procedure, but it is often theresults in validation will decide that a calibration has been performed satisfactory.

4.2.7 Model Validation

Model validation is one of the most important issues in multivariate analysis and developmentof process model. The purpose of model validation is to test the performance of a developedmodel in order to avoid overfitting or underfitting by finding the optimal number and values ofmodel parameters. Here, we need a second data set which is called test or validation data set.It is important that the validation set is closely comparable to the calibration data set withrespect to sampling frequency and condition. The validation set, similar to calibration set, mustcontain a set of representative data for the target population. The only difference betweenvalidation and calibration sets should be the sampling variance. The idea behind the modelvalidation is to evaluate the prediction strength of the model on data with different noise thanthe calibration set. Cross validation is a technique used in chemometric modeling, in which all the availableobjects are used subsequently making models on parts of the data and testing on the otherparts. If we continue and make as many models as there are objects, in such a way that eachtime we leave one of the objects out and use that in validation, we obtain a full crossvalidation. In dynamic time-series modeling, it is not appropriate to apply a full cross validation in thatsense that the data are mixed over the time. It is important to secure a calibration andvalidation set containing time sequence of subsequent data. Hence, the calibration andvalidation data sets must be two different distinct sets of data. There are several indicators and criterion that can be used in order to assess validation of themodel. Naturally, the ability of prediction is the first criterion to consider. A comparisonbetween model output and measurement indicates how well the model can predict the future


58

output. Another indicator is to compare the sum of square errors in prediction with tworeference values. These reference values are a zero-model and an average-model as it isdescribed in chapter 3. The prediction error should consist the error or noise part of the output signal, and henceshould be principally close to a normally distributed noise with a variance smaller than thevariance of output signal itself meaning that the model is better than an average model. Ahistogram plot of error can be used to check the normal distribution of prediction error.Residual Analysis is also another effective method of validation. In this method we analysis theresidual, i.e. prediction error, of the model in order to determine whether there is correlationbetween the prediction error and the inputs. If there are such correlation, it will be anindication of there are still more system dynamics to describe than the model has alreadypicked up. One important remark is that in residual analysis it is assumed that the input isuncorrelated with the disturbances. This means that this analysis will not work for datacollected during feedback.This is an important issue and we have to consider that the data used for calibration of thequality models in this work is collected from a real process during feedback control. Anotherissue to consider is that some variables used in the modes are controlled variables and hencethe variation amplitude is low. This is indeed an indication of the fact that the first assumptionin statistical analysis; i.e. assumption of normal distribution, is more and less violated.


59

4.3 System Delimitation

As it is described in chapter 2, the gasoline processing area consists of different productionunits. In this work, the focus will mainly be on three essential units; catalytic reformer I,catalytic reformer II, and isomerization unit. A simplified flow diagram of this part of gasolineprocessing area is shown in figure 4.1The product streams of all these production units are sent to intermediate product tanks whichare later used as blend components for gasoline blending, as it is shown in more detail in figure2.1 in chapter 2.

HVNTK-38

ReformateNaphtha

Stabilizer/Splitter

Catalytic Reformer I

TK-40

TK-35

HVBN

Isomerization Unit

Isomerate

Naphtha from Condensate Fractionator

Naphtha fromCrude Oil Distillation

Deisopentanizer

LVN


HVN

Reformate

NaphthaStabilizer/

Splitter

Naphtha Stabilizer/Splitter

TK-81

Naphtha fromFractionatorVisbreaking

TK-42

TK-23

LVN

Figure 4.1 : A simplified flow diagram of gasoline processing area.

Basically, in order to be able to optimize the quality of final gasoline products, it is crucial toknow the quality variables of all streams sent to the gasoline blender. Figure 2.1 in chapter 2shows a schematic diagram of all units in gasoline processing area including the gasolineblending components.For some blend components, it is assumed that their qualities do not change over the time andthey can easily be calculated or estimated. For instance, three of the total nine blendcomponents can be considered as almost pure components. These are oxygenate, butane andisopentane. Thus, their qualities can be reasonably estimated based on pure componentproperty. The qualities of two other blend components LVN and LVBN; i.e. light virginnaphtha and light virgin visbroken naphtha, can also be calculated or estimated since they


60

contain light hydrocarbon components, mostly between C5 to C7 molecules, which can beidentified by chromatographic analysis. However, for the reformate products from catalytic reformer units it is not possible tocalculate the qualities easily. It is mainly because these intermediate products containnumerous hydrocarbon components with different molecules structure. The isomerate productfrom isomerization unit contains light hydrocarbon components since the feed to this unit isLVN. Hence, the qualities of isomerate product can be calculated based on identification ofthe hydrocarbon components. Besides, the variation of the qualities, especially the Research Octane Number (RON) quality,in the product streams of the catalytic reformers and isomerization units will particularlyprovide the possibility of producing different gasoline products with more definite octanenumber specification, and thus more optimization potentiality. It is essentially important tohave accurate information of RON quality variable for reformate and isomerate products, sincethese are the high octane number products of the refinery. Furthermore, it is expensive to haveon-line quality measurements for these three intermediate products in order to have the samesampling frequency as the other process variables. The only existing measurement islaboratory analyses which are available only one per day, i.e. a sample rate of 24 hours, foreach quality.As it will be discussed later, the selection of input variables for the quality prediction modelsincludes some temperature variables in the crude oil distillation, condensate fractionator, andthe main fractionator in the visbreaking units, and also flow rate variables in the respectivenaphtha stabilizer and splitters systems. This will extend the system limit to the beginning ofthe gasoline processing area, as it is shown in figure 4.1.Consequently, the prediction of some the qualities will be affected by input variables spreadover the whole processing area and special care should be paid for finding the suitable delayparameters in the obtained model.


61

4.4 Description of Output Variables

In this section a description of desired quality output variables is presented for the models incatalytic reformers and isomerization unit. Among the numerous qualities of gasoline which are officially determined as specifications forthe final gasoline products, we are interested in prediction of the following qualities:

1 Research Octane Number (RON) 2 Motor Octane Number (MON) 3 Reid Vapor Pressure (RVP) 4 Benzene contents of the products (BENZENE)

In the case of MON, there is an extensive lack of measurement which cause a seriouscomplication for prediction modeling of this quality. There is not simply enough measurementfor MON, neither on-line nor laboratory. However, it is possible to take advantage of strongcorrelation between RON and MON, which are basically both measurement of the samequality, i.e. octane number. MON can be predicted by a simple linear regression providedaccurate model for RON available. For this reason, we focus on prediction of RON in thiswork.It is also desired to estimate or predict the yield of reformates and isomerate products for eachreformer and isomerization unit. The desired reactions in these units are dehydrogenization,cyclization and isomerization. However, hydrocracking and condensation reactions may alsotake place in which the first one will produce light hydrocarbons and the second will causeformation of coke. As a results, light hydrocarbon components like methane, ethane, propane,and butane will be produced which is later removed in stabilizer column. Consequently, theyield of reformate will be reduced. The change in the yield is thus correlated with RVP, andyield of reformate can be calculated as the following:

Yield = Reformate flow rate

Reformer feed flow rate⋅ 100 ⋅ CORR (4.1)

where:CORR = C1 − C2 RVPC3 (4.2)

in which C1 , C2 , and C3 are constants. Reformate flow rate product and the feed flow rate tocatalytic reformer are both measured. CORR in equation 4.2 is a correction factor used inequation 4.1 to compensate for RVP changes. Figure 4.2 shows the correction factor for aperiod of seven months operation in catalytic reformer I. The calculation of CORR isperformed by using an on-line RVP analyzer in this unit. In table 4.1, the average, standarddeviation, maximum, and minimum of CORR is shown. As it can be seen the correlation factor has an average of 0.954 in this period with a standarddeviation of 0.005. As a result, the correlation factor is a weak function of RVP. Thischaracteristic is also observed in catalytic reformer II. It is desired to develop a model for RVP in which the model can be used in calculation ofyield. Consequently, there will be no need for a separate model for yield of production since itcan be calculated using the existing measurement for feed flow rate and reformate flow rate,and then apply the predicted value of RVP model for calculation of the correction factor. As described in chapter 2, the feed to isomerization unit is LVN, containing light hydrocarbonmolecule. The benzene contents of LVN is low, and cyclization reactions is expected to takeplace only in a small extend in this unit. Thus, the contents of benzene in isomerate product is


62

expected to be small and mainly unchanged. Laboratory analyses for a period of 14 monthsoperation has shown that the benzene content has been zero for a large period of time. Thereare only 54 non-zero measurements reported with an average of 0.17 wt.%. and standarddeviation of 0.13. Hence, there will be no need for prediction model for benzene contents ofisomerate product and i will be assumed to be constant less than 0.2 wt%.

0.93

0.94

0.95

0.96

0.97

0.98

Sample

CO

RR

CORR for 7 Months Operation in Reformer I

Figure 4.2: Correction factor used in equation 4.1 for calculation of yield of reformate productin catalytic reformer I.

CORR Factor

Average 0.954

Standard Deviation 0.005

Maximum 0.973

Minimum 0.938

Table 4.1: Statistic value for correction factor.

Hence, in this work there will be focused on development of chemometric model forprediction of RON, RVP, and benzene contents for the reformate products and RON and RVPfor the isomerate product..The output variables for catalytic reformer I, II, and isomerization unit is shown in table 4.24.3, and 4.4 along with the calculated average, standard deviation, maximum, and minimumvalues. These values are for calibration and validation data sets after removal the outliers. Themaximum and the minimum values for each quality can be compared with the interval of[avg.-3*std, avg+3*std] in order to assess the outliers. Equation 4.3 indicates that for anormally distributed variable the probability that a value can be out of the range is lessµ ± 3σthan 1%. Here, the mean value and standard deviation are denoted by µ and σ. Equation 4.3 isa results of Camp-Meidels theorem (L. Broendum and J.D. Monrad, 1987).

P( X − µ ≥ 3σ) = 0.27% ⇔ P( X − µ < 3σ) = 99.73% (4.3)


63

Hence, it is expected that only one percent of data will fall out of the ranges as shownµ ± 3σin the tables 4.1, 4.2, and 4.3. Furthermore, it can be seen that the deference between maximum and minimum values ofRON is 2 for all the two reformer units and three for isomerization unit. This is in fact anindication of effective feed-back control of RON. The effect of closed-loop control isdiscussed in chapter 3.

Catalytic Reformer I

Calibration Validation

RVP RON BENZENE RVP RON BENZENEAVG. 49.67 99.97 3.53 50.85 99.97 3.74

STD 3.02 0.37 0.43 3.74 0.45 0.36

MAX. 56.00 101.60 4.91 61.00 101.50 4.37

MIN. 39.00 98.60 2.12 44.00 98.30 2.95

AVG. + 3STD 58.72 101.09 4.82 62.05 101.33 4.83

AVG. - 3STD 40.61 98.85 2.24 39.65 98.61 2.66

Table 4.2: Output variables in Catalytic Reformer I.

Catalytic Reformer II


RVP RON BENZENE RVP RON BENZENEAVG. 37.06 101.00 1.79 37.90 101.00 1.76

STD 3.73 0.25 0.45 3.46 0.20 0.43

MAX. 50.00 101.80 2.80 47.00 101.60 2.42

MIN. 23.00 100.00 0.60 32.00 100.40 1.16

AVG. + 3*STD 48.26 101.76 3.14 48.28 101.58 3.05

AVG. - 3*STD 25.86 100.25 0.44 27.51 100.41 0.47

Table 4.3: Output variables in Catalytic Reformer II.

Isomerization Unit


RVP RON RVP RONAVG. 70.04 87.29 70.20 87.24

STD 3.54 0.47 2.98 0.32

MAX. 76.30 88.60 81.00 88.40MIN. 58.70 85.70 65.50 86.50

AVG. + 3STD 80.65 88.70 79.13 88.21

AVG. - 3STD 59.43 85.88 61.28 86.27

Table 4.4: Output variables in isomerization unit.


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4.5 Description of Input Variables

The described procedure in section 4.2.2 for selection of the appropriate input variables isfollowed in order to obtain a set of data which is informative enough with respect to a modelset that can be determined from the data using appropriate chemometric methods. In the following subsections the variables selected for the models will be described. Thesevariables are going to be used for the RON, RVP, and benzene models described in chapter 5.

4.5.1 Input Variables for Catalytic Reformer I

As it is described in chapter 2, the feed to catalytic reformer I is a mix stream of heavy virginnaphtha (HVN) from splitter in crude oil distillation section and heavy virgin visbrokennaphtha (HVBN) from the splitter in visbreaking section. Figure 4.3 shows a simplified flowdiagram of catalytic reformer I along with the stabilizer/splitter system in crud oil distillationand in after the mail fractionator in the visbreaking section. Table 4.5, 4.6 show a list allvariables that are used in developing the chemometric models described in chapter 5 forprediction of RON, RVP and benzene contents of the reformate product. The values ofcalculated average, standard deviation, maximum, and minimum along with the values of

are shown in tables 4.5 and 4.6 for respectively calibration and validation data sets.µ ± 3σ

C-401Stabilizer

Offgas

Liquid Gas

Reformate

Reflux

PF Flow Rate H-402

R-401 R-403R-402 R-404

Separator

C-401 FeedReboiler

R1 Outlet Temp. R2 Outlet Temp. R3 Outlet Temp.

H2 Gas

LVBN

C-652Splitter

Stabilizer

Gas

Visbreaking Main Fractionator

C-601

Naphtha

Crude Oil Distillation

C-203 Splitter

Stabilizer

Naphtha

Gas

HVN

LVN

HVBN

Figure 4.3 : A simplified flow diagram of catalytic reformer I in gasoline processing area.


65

Calibration

No. Description Unit AVG. STD MAX. MIN. AVG. +3STD

AVG. -3STD

1 H / C mol/mol 3.86 0.42 6.86 3.00 5.12 2.61

2 % H2 Gas % 73.22 1.82 80.70 59.23 78.68 67.75

3 R1 Outlet Temp 0C 430.92 4.21 442.45 421.67 443.54 418.31

4 R2 Outlet Temp 0C 471.10 4.62 482.62 460.40 484.95 457.25

5 R3 Outlet Temp 0C 500.33 3.54 507.32 489.89 510.95 489.71

6 Reformer FeedFlow Rate

m3/hr 51.38 7.27 63.06 29.87 73.17 29.58

7 Reformate FlowRate

m3/hr 38.09 5.85 48.45 21.09 55.64 20.53

8 C401 Liquid GasFlow Rate

m3/hr 5.37 0.96 8.08 1.47 8.25 2.50

9 C401 Reflux FlowRate

m3/hr 23.06 1.05 25.33 20.99 26.22 19.90

10 C401 Feed Temp 0C 165.45 2.86 174.05 158.34 174.03 156.87

11 C401 ReboilerTemp

0C 254.59 2.11 261.57 239.98 260.94 248.25


m3/hr 27.72 6.21 39.02 13.04 46.35 9.10

13 HVN Flow Rate m3/hr 52.79 8.28 76.57 23.69 77.63 27.94

14 LVN Flow Rate m3/hr 36.97 6.85 66.55 17.84 57.52 16.42

15 HVBN Flow Rate m3/hr 10.74 2.96 18.36 2.34 19.63 1.85

16 CP201 0C. 102.33 5.43 113.72 83.23 118.63 86.04

17 CP601 0C. 112.86 8.38 134.80 91.63 138.00 87.72

18 CP203B 0C 105.52 2.59 114.62 91.65 113.30 97.74

19 CP652B 0C 101.76 4.12 130.76 71.42 114.11 89.40

Table 4.5: Input variables used for calibration of the models in catalytic reformer I.

The first 5 variables listed in table 4.5 are expected to have a large effect on RON quality. H/Cis the ratio of mole hydrogen in the recycle gas per mole hydrocarbon in the feed. Variablenumber 2 %H2 is the H2 purity in %mole or %volume in the recycle gas from the productseparator to the feed stream of the reformer. These two variables indicate the developed H2

during the reactions. It is expected that a change in the feed composition will be reflected inthe H/C mole ratio.Variables number 3, 4, and 5 are the outlet temperature of the reactor number 1, 2, and 3respectively. These temperatures indicates the type of the reactions take place in the reactors,since the hydrocracking and condensation reactions will occur at higher temperature.Variables number 6 and 7 are the feed flow rate to the reformer and the reformate productflow rate.


66

Variation in RVP is dependent on the light hydrocarbon contents of reformate product, andthus, it is sensitive to the operation of the stabilizer C401. Hence, variables 8, 9, 10, and 11are chosen from stabilizer C401. The description of these variables in the table 4.5 and 4.6 areself explanatory. Variable number 12 is the reflux flow rate in the splitter column C203, whichaffects the changes in the boiling range of the LVN top product in C203 and hence, the split ofthe naphtha feed to LVN and HVN. Variables number 13, 14, 15, are flow rate of LVN,HVN, and HVBN.

Validation


AVG. - 3STD

1 H / C mole/mole 3.96 0.47 6.17 3.26 5.36 2.56

2 % H2 Gas %mole 72.52 1.79 79.31 63.07 77.90 67.14

3 R1 Outlet Temp 0C 436.45 3.58 444.30 426.58 447.20 425.69

4 R2 Outlet Temp 0C 480.89 4.24 490.08 469.46 493.61 468.17

5 R3 Outlet Temp 0C 506.61 4.94 517.99 496.46 521.44 491.79


m3/hr 51.44 6.03 62.66 36.76 69.54 33.34

7 Reformate FlowRate

m3/hr 39.02 4.18 47.62 27.62 51.55 26.48

8 C401 Liquid GasFlow Rate

m3/hr 4.57 0.92 7.09 1.04 7.32 1.82


m3/hr 21.66 1.25 28.92 16.81 25.43 17.90

10 C401 Feed Temp 0C 165.15 3.59 173.50 156.76 175.93 154.37


0C 254.51 1.97 258.02 246.49 260.42 248.60


m3/hr 31.05 4.66 38.89 17.90 45.04 17.06

13 HVN Flow Rate m3/hr 54.80 5.57 69.51 35.81 71.50 38.10

14 LVN Flow Rate m3/hr 32.09 7.28 53.02 14.00 53.92 10.27

15 HVBN Flow Rate m3/hr 55.43 6.32 67.57 43.00 74.38 36.48

16 CP201 0C. 11.47 2.72 17.85 3.29 19.63 3.30

17 CP601 0C. 105.24 4.81 114.15 91.93 119.66 90.82

18 CP203B 0C 111.27 7.91 131.48 91.70 135.00 87.53

19 CP652B 0C 106.47 2.31 115.89 100.84 113.42 99.53

Table 4.6: Input variables used for validation of the models in catalytic reformer I.

A change in the composition of the crude oil can affect the fraction of HVN and LVN in thesplitter. This change is reflected by the temperature on the naphtha side stream in crude oildistillation. Variable number 16, CP201, which is also called as cut point temperature, is a


67

pressure corrected temperature of naphtha side stream tray in crude oil distillation, which iscalculated as in equation 4.4.

Tcut = (T i ) C1 − C2Ln(Pi)C1 − (Ti )(Ln(Pi))

(4.4)

where C1, and C2 are constants, Ti is the measured temperature in Kelvin, and Pi is toppressure in bar absolute.Variables number 17, 18, and 19 are calculated by using equation 4.4 for the temperature ofnaphtha from main fractionator in visbreaking section, bottom temperature of splitter in crudedistillation, and bottom temperature of splitter in visbreaking section respectively.

4.5.2 Input Variables for Catalytic Reformer II

There are a lot of similarity between the process in catalytic reformer I and II. Unless othermentioned, the description of the variables are the same as for the reformer I.The feed to catalytic reformer II is HVN from splitter C-4703 as shown in figure 4.4, whichshows a simplified flow diagram of catalytic reformer II along with the stabilizer/splittersystem after condensate fractionator. Table 4.7, 4.8 show a list all variables that are used indeveloping the chemometric models for prediction of RON, RVP and benzene contents of thereformate product. Table 4.7, 4.8 shows average, standard deviation, maximum, and minimumalong with the values of as well for calibration and validation data sets respectively.µ ± 3σ

SeparatorR3 Outlet

R-4401 R-4402 R-4403

H2H-4401

R1 Outlet R2 Outlet

Reflux

HVN

C-4703Splitter

CondensateFractionator

Stabilizer

Crude Oil Distillation

HVN

Reflux

C-4401 Feed

Reboiler

Reformate

C-4401

LVN

LVN

Naphtha

Naphtha

Reboiler

RF Feed Stream

Figure 4.4 : A simplified flow diagram of catalytic reformer II in gasoline processing area.


68

The first 5 variables listed in table 4.7 are chosen from the reactors and the recycle gas fromthe reformer which are expected to have a large effect on RON quality as it is explained inreformer I. Variation in RVP is dependent on the operation of stabilizer C4401. Hence, variables 7, 8, 9,10, and 11 are chosen from stabilizer C4401. Variable number 12, 13 , and 14 are chosen fromthe splitter C4703 which affect the split of naphtha feed to LVN and HVN. Variables 15, 16,17, are calculated by using equation 4.4. The description of these variables in the table 4.7 and4.8 are self explanatory.

Calibration

No. Description Unit AVG STD MAX MIN AVG +3STD

AVG - 3STD

1 R1 Outlet Temp 0C. 391.80 3.28 398.77 380.81 401.65 381.95

2 R2 Outlet Temp 0C. 446.91 5.36 458.23 432.86 462.99 430.84

3 R3 Outlet Temp 0C. 472.33 4.98 482.95 459.88 487.26 457.40

4 H/C mole/mole 4.42 0.73 6.61 3.51 6.60 2.23

5 H2 Purity %mole 82.47 1.54 87.36 72.82 87.10 77.85


m3/hr 92.41 10.66 107.98 64.99 124.38 60.44

7 C4401 Feed Temp 0C. 187.47 3.42 194.63 158.52 197.73 177.20


0C. 248.82 1.52 252.85 203.60 253.39 244.26

9 Reformate ProductFlow Rate

m3/hr 76.29 8.85 89.21 54.16 102.85 49.73


m3/hr 4.98 1.76 11.53 0.61 10.26 -0.29

11 C-4401 Feed FlowRate

m3/hr 77.81 9.18 91.36 54.00 105.36 50.27


m3/hr 119.33 9.26 146.00 68.03 147.10 91.56

13 C4703 LVN FlowRate

m3/hr 76.77 3.29 89.10 21.41 86.64 66.91

14 C4703 ReboilerSteam Flow Rate

ton/hr 17.68 1.19 20.00 12.48 21.26 14.11

15 CP201 0C. 103.62 5.45 113.90 83.23 119.98 87.26

16 CP4201 0C. 101.26 3.80 123.64 71.64 112.65 89.88

17 CP4703B 0C. 110.10 1.31 113.48 78.29 114.02 106.18

Table 4.7: Input variables used for calibration of the models in catalytic reformer II.


69

Validation


AVG - 3STD

1 R1 Outlet Temp 0C. 397.61 2.71 403.82 391.92 405.74 389.49

2 R2 Outlet Temp 0C. 456.99 4.62 465.29 448.60 470.84 443.14

3 R3 Outlet Temp 0C. 482.32 6.25 493.09 471.82 501.09 463.56

4 H/C mole/mole 4.48 0.43 5.66 3.73 5.77 3.20

5 H2 Purity %mole 80.53 1.55 84.46 69.82 85.19 75.88


m3/hr 90.86 9.76 103.16 75.45 120.15 61.58

7 C4401 Feed Temp 0C. 182.97 4.05 188.64 171.90 195.11 170.82


0C. 247.93 1.54 250.41 243.58 252.54 243.33

9 Reformate ProductFlow Rate

m3/hr 74.89 7.50 87.46 63.10 97.37 52.40


m3/hr 5.91 2.33 11.25 1.86 12.91 -1.09

11 C-4401 Feed FlowRate

m3/hr 76.50 8.07 87.61 63.91 100.71 52.29


m3/hr 117.74 4.12 127.91 89.99 130.11 105.38

13 C4703 LVN FlowRate

m3/hr 76.55 3.03 86.46 60.76 85.65 67.44

14 C4703 ReboilerSteam Flow Rate

ton/hr 17.90 0.73 19.28 13.17 20.08 15.72

15 CP201 0C. 103.50 5.21 114.15 91.93 119.14 87.85

16 CP4201 0C. 100.61 1.94 106.21 95.84 106.44 94.78

17 CP4703B 0C. 110.75 0.94 113.56 108.13 113.57 107.93

Table 4.8: Input variables used for validation of the models in catalytic reformer II.


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4.5.3 Input Variables for Isomerization Unit

The feed to isomerization unit is light virgin naphtha (LVN) after removal of isopentane (IC5)in deisopentanizer (DIP) as it is described in chapter 2. LVN is the top product of the splitterC4703 which is sent to DIP, as it is shown figure 4.5. A typical LVN contains mostly ofhydrocarbon molecules between C5 to C7 with a True Boiling Point (TBP) range of 32-88 0C.Hence, it would be possible to identify the hydrocarbon components in the feed to this unit bychromatographic analysis. The low octane LVN is converted to high octane number isomerate product by catalyticisomerization process. The reactions in this process are mainly exothermic. Table 4.9, and 4.10 show a list all variables used for model development in this unit. Thesemodel are developed for prediction of RON, and RVP. The benzene contents of the isomerateproduct is assumed to be contestant. The values of calculated average, standard deviation,maximum, and minimum along with the values of are shown in tables 4.9 and 4.10 forµ ± 3σrespectively calibration and validation data sets.

LVN from Deisopentanizer

Extract from Molex Unit

H2 from Reformers

IsomerateMolex Unit

R-4601 AR-4601 B C-4601

Stabilizer

Stabilized Naphtha

HVN

C-4703Splitter

LVN

Reflux

DIP

IC5Reflux

Figure 4.5 : A simplified flow diagram of isomerization unit in gasoline processing area.

Variable number one is the inlet temperature of the feed to the reactor A. The outlet stream ofthe reactor A is cooled down to about the same temperature as the feed to the first reactor andsent to reactor B. Variables 2, and 3 are outlet temperatures of the reactors. Variable number4 is Liquid Hourly Space Velocity (LHSV) which is calculated as the total inlet flow rate ofthe feed to the reactors divided by the catalyst volume. Variable number 5 is the hydrogenconsumption in this unit, since the isomerization reactions consume H2. Variables 6. 7. 8. and


71

9 contain information about the operation in DIP in which the IC5 is removed, and thus thesevariables will reflect de degree of efficiency in DIP.

Calibration


AVG - 3STD

1 Reactor InletTemp

0C 142.96 2.21 147.30 100.27 149.60 136.32

2 Reactor A OutletTemp

0C 189.10 2.28 193.81 132.52 195.95 182.25

3 Reactor B OutletTemp

0C 159.80 2.52 164.20 112.18 167.35 152.26

4 LHSV 1/hr 2.15 0.14 2.29 1.50 2.58 1.72

5 H2 Consumption Sm3/hr 2553.09 245.48 3136.48 1563.97 3289.53 1816.65

6 DIP Tray 8 Temp 0C 84.88 1.28 92.53 81.59 88.72 81.03

7 DIP BottomFlow Rate

m3/hr 55.63 3.40 60.59 41.03 65.83 45.44

8 DIP Feed FlowRate

m3/hr 75.54 2.91 83.05 60.44 84.27 66.81

9 DIP Reflux FlowRate

m3/hr 98.18 8.50 152.48 65.96 123.68 72.68

10 CP4703T 0C 52.46 1.79 57.56 37.68 57.83 47.09

11 C-4703 RefluxFlow rate

m3/hr 124.24 3.38 146.00 87.57 134.39 114.09

12 C-4703 FeedFlow Rate

m3/hr 172.69 12.09 193.77 112.81 208.97 136.42

Table 4.9: Input variables used for calibration of the models in isomerization unit.

Variables number 10 is the LVN cut point in the splitter C4703 calculated by using equation4.4. Variables 10, 11, and 12 together with variable number 7 which is in fact the flow rate of LVNcontain information about the mass balance and split efficiency in the splitter C4703.


72

Validation


AVG. - 3STD

1 Reactor InletTemp

0C 143.40 1.09 147.72 131.12 146.67 140.13

2 Reactor AOutlet Temp

0C 189.35 1.54 193.11 175.91 193.98 184.72

3 Reactor BOutlet Temp

0C 159.74 1.04 162.50 147.22 162.86 156.62

4 LHSV 1/hr 2.18 0.07 2.27 1.44 2.40 1.95

5 H2 Consumption Sm3/hr 2787.02 176.93 3183.27 1706.59 3317.79 2256.24

6 DIP Tray 8Temp

0C 85.33 1.49 89.30 76.55 89.79 80.87

7 DIP BottomFlow Rate

m3/hr 55.81 3.33 59.20 10.89 65.81 45.82

8 DIP Feed FlowRate

m3/hr 75.39 2.82 84.19 53.58 83.85 66.93

9 DIP Reflux FlowRate

m3/hr 96.98 14.73 144.71 24.63 141.18 52.78

10 CP4703T 0C 53.94 1.33 57.66 50.96 57.93 49.95

11 C-4703 RefluxFlow rate

m3/hr 112.28 7.60 127.91 89.99 135.08 89.47

12 C-4703 FeedFlow Rate

m3/hr 172.75 11.04 189.34 129.98 205.87 139.64

Table 4.10: Input variables used for validation of the models in isomerization unit.


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4.6 Selection the Sample Interval

In most of the modern industry process control system today, one or another type ofcommercial Distributed Control System (DCS) is used in which the conventional processvariables such as temperature, pressure and flow rate are measured in a sample rate of a fewseconds. This high frequency sampling rate is due to important consideration of processcontrol applications, and occur at the lowest level of conventional control instrumentationwhich is then connected normally to the Control Processor of the respective control loop. Thedata acquisition system will then collect the data and possibly perform a kind of suitable datatreatment later. This data treatment can be such as a moderate filtering in order to preventaliasing in process control, or eliminate obvious sensor fault.

Right from the beginning of every input/output modeling work or any process controlapplication the question about sampling frequency will arise. How fast should a sampling ratebe in order to data would then be informative enough to meet the demands for a robustprediction model?. This question is closely related to the dynamic characteristic of the system under study.Furthermore, it is not always possible to measure the desired quality variable considering thepossibility and limitation of measurement devices and what existing hardware and softwaresystem may offer in the data sampling field. Hence, the question above is effectively related toa second question about the possibility of whether we can actually get a set of measurementsin a suitable sample frequency which we desire. It is attempted to answer these questions in the following subsections.

4.6.1 Suitable Sample Frequency

An appropriate sampling rate should be relative to the time constants of the system. A goodchoice can be a sample frequency of ten times of the bandwidth of the system (Ljung, L.1987). In the frequency domain, the dynamic behavior of a system is characterized by itsbandwidth. There is a reciprocal relationship between bandwidth and dynamic response time.For a first order dynamic system the bandwidth is equal to natural frequency of the system,this means that the product of bandwidth and dynamic response time is exactly one. Friedland(Friedland, B. 1987) has shown that this product is approximately one for a properly dampedsecond order system. The same relation is also valid for higher system order as well. On the other hand, very fast sampling is undesirable since the developed model fits in highfrequency bands, and hence produce bias in model prediction. Besides, fast sampling leads tonumerical difficulties in model parameter estimation.

4.6.2 Sample Frequency for Input Variables

The input signals are mostly temperature, pressure and flow rate and also some calculatedvariables based on these measurements, as it is described in chapter 4. The data acquisition system of the refinery offer 4 sampling rates which are average of 3 and 6minutes data, average of one hour, and average of one day data. As it is described in chapter 4, we are seeking the relevant effect of some process variables onthe qualities of intermediate gasoline products after reforming and isomerization units. Thus,our system-limit covers the whole gasoline processing area from the naphtha side-stream of


74

crude oil distillation column in the beginning of this processing area to the intermediatestorage tank in gasoline blending at the end.The question is, what is a good estimate for bandwidth and dynamic response time of thissystem? or more practically which of those existing 4 sample frequencies should be selected inorder to be around 4-10 times higher than the bandwidth of this system? Notice that, for example, in catalytic reformer I, there are 4 reactors, 1 distillation column, 1heater, and 1 gas-liquid separator. Consequently, we may think of several hours of responsetimes. Based on the above considerations, the sample rate of average of one hour is chosen for theinput variables in order to satisfy the demand for a sampling rate of 4-10 times faster than theresponse of the system. This choice rely on some previous practical experience in modeling inthis project, and also in previous control application at the refinery. These experiences suggestthat day-average sampling rate is too slow and six-minutes sampling rate is too fast.

4.6.3 Sample Frequency for Output Variable

The qualities of reformates and isomerate products, which make the output signal of themodels, are measured at laboratory once every 24 hours. This low sampling frequency formodel output has given rise to a challenging problem in this work. It may appear, at the firstplace, that in some modeling cases, it would not simply be possible to obtain a reliable androbust model by this low sampling frequency. The proposed solution for output low sample frequency is that we simply consider thesampling rate of the system to be one hour, in which we have a lot of missing data in outputmeasurement. And then, depending on the variation in output signal from one day to another,we can choose one of the following way to overcome this issue.If the output variation is slow moving over one day to the next day, this is as the case of RON,we can perform an interpolation in output and perform model calibration but avoidinterpolation in model validation. In the opposite case, in which there is a considerable variation in the output signal, indicating apossible faster dynamic response, such as the case of RVP, it would not be a good idea toreplace the missing output by interpolation. The proposed solution here is we choose asuitable structure for ARX model in which we take hourly sampled input together with the lastexisting output signal in order to model the prediction of output at time t. Since this solution isinherently integrated in the ARX structure, it will be described in the following section.


75

4.7 PCA Analysis

PCA model is developed in order for assessment of representability of data used for thedeveloped models. It is important to analysis the data to discover any abnormality in the datawhich can for instance be a departure from the normal operation point. It is assumed thatoutliers are already removed and thus the abnormality can be due to an operation point whichis not normal or is shutdown or startup period. Another aspect of a PCA model is to examinethe existence of distinct clusters of data which suggest totally different operation of the plant.In this case it should be considered to develop prediction models for each area separately. Athird aspect is to discover any collinearity in the selected input.The PCA analysis is performed for the input data which is used for the development of thechemometric models for catalytic reformer I. In the next subsection a description of the PCAmodel is presented.

4.7.1 PCA Model for Catalytic Reformer I

The input to the PCA model is called X matrix. Number of selected input variables for theprediction models for this unit are 19 as it is described in section 4.5. Hence, the data Xcontains 19 columns. Furthermore, the data X contains both the calibration and the validationsets used in the prediction model development, and hence number of rows in X matrix, whichis denoted by n in equation 4.5, corresponds to the total number of data after removing thefaulty, and outliers. Number of n is 10012 samples. The input X data is then autoscaled. Thecovariance matrix of X is calculated by equation 4.5, since the data is autoscaled this equationwill give the correlation matrix.

cov(X) = XTXn − 1

(4.5)

As it is described in chapter 3, PCA model relies on an eigenvector decomposition of thecorrelation matrix of the data X. The eigenvectors are called Principal Components (PC), andthe associated eigenvalues of the correlation matrix are a measure of the captured variance foreach pair of score and loading vector. Principal Components are also called Latent Variables(LV).In table 4.11, the percent variance captured by each PC is shown for the PCA analysis. Figure4.6 shows the eigenvalues of the correlation matrix versus principal component number.These information is used in order to decide how many PCs should be included to the model.It appears that a number of 10 PCs can be a suitable choice. This choice rely on an assessmentof the level of the noise in the data, and it is expected that most of the samples in input datareflect the interesting operation points, as shown in the tables 4.5 and 4.6.

A graphical approach is the best way to represent the results of a principal component analysiswhich makes the interpretation of the results much easier. By examining scores and loadingplots, we can explore the quality of substantial information in the data. We can examine thescores and loadings plot one by one or plot the score or loading vectors for PC number 1versus PC number 2. Figure 4.7 shows the scores on PC number 1 along with 95 % limit of confidence interval. Thescores are the effect of observations on the PC. Figure 4.8 shows a scatter plot of the scoresfor PC number 1 versus the scores for PC number 2 along with the 95% and 99% confidence


76

interval limits. These two figures shows no significant outliers, and the major part of the datais indeed inside the 95% limit.


PrincipalComponent Number

Eigenvalue ofCorrelation (X)

%Variance Capturedby this PC

%VarianceCaptured Total

1 4.84E+00 25.49 25.49

2 3.41E+00 17.96 43.44

3 2.73E+00 14.35 57.79

4 2.21E+00 11.65 69.44

5 1.28E+00 6.73 76.18

6 1.07E+00 5.61 81.79

7 7.51E-01 3.95 85.74

8 6.33E-01 3.33 89.07

9 4.79E-01 2.52 91.59

10 3.60E-01 1.90 93.49

11 3.22E-01 1.70 95.18

12 2.93E-01 1.54 96.73

13 2.37E-01 1.25 97.97

14 1.32E-01 0.70 98.67

15 9.26E-02 0.49 99.15

16 8.51E-02 0.45 99.60

17 5.61E-02 0.30 99.90

18 1.42E-02 0.07 99.97

19 5.20E-03 0.03 100.00

Table 4.11 : Percent Variance Captured by PCA Model. What we observe in the figures is that there is apparently a systematic variation in data, andthere are at least two major areas of operation. It is an indication of two different operationmodes. It is important for the task of the modeling that it is necessary separate these twooperation modes and develop model for each mode alone.The interesting observation is that the periods of these two operation modes are not the same,meaning that the operation points are independent of season changes. This indication suggeststhat the operation modes are mainly related to the desired quality of RON and benzenecontents rather than RVP. The specification for RVP quality is different for summer andwinter periods, but there is no season change for specification of neither RON nor benzenecontent. There are two major type of reformate products regarding the level of benzenecontent characterized by low and high aromatic; i. e. mostly benzene, contents. Examining thefigures shows that the change from one to another variant is around a few weeks. Consequently, it is not necessary to distinguish between these two regions and it should beinvestigated that one model for both operation modes will be appropriate.


77

0 5 10 15 200

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3

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5Eigenvalue vs. PC Number

PC Number

Eig

enva

lue

Figure 4.6 : Percent variance Captured by PCA model .

0 2000 4000 6000 8000 10000 12000-6

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Sample Scores with 95% Limits

Figure 4.7 : Scores on PC number 1.


78

Figure 4.9 shows the loadings for PC number 1 versus number 2. The loading plot exhibit theeffect of variables on the PC. Examining the loading plot is interesting to discover whichvariables have the most effect on the PC. It can be seen that for example variables 6 and 7,which are flow rate of the feed to the reformer and the reformate product, have the sameeffect on both PCs, meaning that they are correlated, and thus one of them is enough to beincluded in a model to represent the corresponding information.

-10 -5 0 5 10-6

-4

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6Catalytic Reformer I

Component 1

Com

pone

nt 2

Figure 4.8 : Scatter plot of PC # 1 vs. PC # 2 showing the 95% and 99% limits .


79

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3-0.4

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form

er I

, Loa

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Reformer I, Loadings for PC# 1 versus PC# 2

Figure 4.9 : Loading for PC number 1 and 2.

4.7.2 PCA Model for Catalytic Reformer II

The input to the PCA model is X matrix containing 17 columns, representing 17 variables usedin models for reformer II, and 9703 rows for the total number of existing objects. The input Xdata is autoscaled, and contains both the calibration and the validation sets used in theprediction model development.

Table 4.12 shows the percent variance captured by each PC in the PCA analysis. Figure 4.10shows the eigenvalues of the correlation matrix versus principal component number. It thiscase, it can be seen that the choice of PC is in the region of the 4-8. To avoid loss ofsignificant information 7 PCs is chosen to be included in the model.Figure 4.7 shows the scores on PC number 1 along with 95 % limit of confidence interval. Thescatter plot of the scores for PC number 1 versus the scores for PC number 2 along with the95% and 99% confidence interval limits is shown in figure 4.8. These two figures shows nosignificant outliers, and the major part of the data is indeed inside the 95% limitExamining these figures shows a systematic variation in data, indicating two differentoperation modes. The period of these two operation modes are much less than the period incatalytic reformer I and is around 10 days. This suggests again that the operation modes arerelated mainly to the desired quality of RON and benzene contents rather than RVP. Theconclusion is again that it is not appropriate to separate this two regions.


80




%VarianceCaptured by this PC


1 7.21E+00 44.02 44.02

2 3.02E+00 18.42 62.44

3 2.50E+00 15.28 77.72

4 9.22E-01 5.63 83.35

5 7.62E-01 4.65 88.01

6 5.99E-01 3.66 91.66

7 3.53E-01 2.16 93.82

8 2.70E-01 1.65 95.47

9 2.22E-01 1.36 96.83

10 1.86E-01 1.13 97.96

11 1.19E-01 0.73 98.69

12 1.04E-01 0.63 99.32

13 6.16E-02 0.38 99.70

14 4.12E-02 0.25 99.95

15 5.63E-03 0.03 99.98

16 2.13E-03 0.01 100.00

17 6.73E-04 0.00 100.00

Table 4.12 : Percent Variance Captured by PCA Model

0 5 10 15 200

1

2

3

4

5

6

7


PC Number

Eig

enva

lue

Figure 4.10 : Eigenvalue versus PC number.


81

0 2000 4000 6000 8000 10000-6

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6

Sample Number

Sco

re o

n P

C#

1



The loadings for PC number 1 versus number 2 is shown in figure 4.13, indicating the effect ofvariables on the two PCs. It can be seen that for example variables 6 , 9 and 11, which areflow rate of the feed to the reformer, feed to the stabilizer, and the reformate product, havethe same effect on both PCs. The correlation means that one of them is enough to be includedin this PCA model. Notice that these variables are used in different prediction models, which can have differentrepresentation of the dynamic information.


82

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6Catalytic Reformer II

Component 1

Com

pone

nt 2


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Reformer II; Loadings for PC# 1

Ref

orm

er II

, Loa

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s fo

r PC

# 2

Reformer II, Loadings for PC# 1 versus PC# 2

Figure 4.13 : Loading for PC number 1 and 2.


83

4.7.3 PCA Model for Isomerization Unit

The input to the PCA model is X matrix containing 12 columns for the 12 variables used inprediction models for isomerization unit, and 9467 rows for the total number of objects. Theinput X data is autoscaled.




%VarianceCaptured by this PC


1 5.36E+00 44.65 44.65

2 2.20E+00 18.32 62.97

3 1.50E+00 12.47 75.44

4 9.93E-01 8.27 83.71

5 6.77E-01 5.64 89.35

6 4.00E-01 3.34 92.69

7 3.14E-01 2.62 95.31

8 2.06E-01 1.71 97.02

9 1.50E-01 1.25 98.27

10 1.09E-01 0.91 99.18

11 7.29E-02 0.61 99.79

12 2.56E-02 0.21 100

Table 4.13 : Percent Variance Captured by PCA Model

Figure 4.14 and table 4.13 show the eigenvalues of the correlation matrix versus principalcomponent number and percent variance captures by each PC. Based on these information. achoice of 6 PCs is suitable for the PCA model in this case. The plot of scores on PC number one, which is shown in figure 4.15, indicate that there aresome objects that are out of the range of 95% limit of confidence interval. These objects arenot outlier and identified to be from an operation point in which the temperature of the inletstream to the first reactor and the temperature of both outlet streams are lower than the rest ofthe objects. The amount of data in this region is 12% of total number of data including bothcalibration and validation which consist of 9467 hours operation (about 13 months). Thisabnormality has obviously occurred in several periods mostly in calibration data as it can beseen in figure 4.15. It is more clear in figure 4.17 which shows the scatter plot of the scoresfor PC number 1 versus the scores for PC number 2 along with the 95% and 99% confidenceinterval limits. Figures 4.16, and 4.18 shows the corresponding plot for scores on PC number 2, and a scatterplot scores on PC number 2 versus PC number 3 respectively. A comparison between figure4.15 and figure 4.16 indicate that the abnormality is captured mostly by the first PC. However,figure 4.16 suggest that there is clear systematic variation in data indicating existence ofdifferent operation modes as in the reformer units.Whatever reason for this abnormality may be, it will not affect the development of theprediction models since that portion of data should be excluded from the calibration set andhence the obtained model will be valid only for the normal operation point.


84

0 2 4 6 8 10 120

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Eig

env

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Figure 4.14 : Eigenvalue versus PC number.

0 2000 4000 6000 8000 10000-15

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85

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The loadings for PC number 1 versus number 2 is shown in figure 4.19 indicating the effect ofvariables on the two PCs. It can be seen that variables 1, 2, 3, 4, 5, 7, 8, and 12 have thestrongest effect on PC number one, and it is thus expected that these variables have the largesteffect on the abnormality described before and observed in figures 4.17 and 4.15. Adescription of these variables can be seen in table 4.9.Variables 1 through 5 represent the operation in the reactors. It is interesting to discover thatvariables 7, 8, and 12 which are the flow rate of DIP bottom, DIP feed, and splitter feed, hasalso an effect on the abnormality. Examination of the data in the period of abnormality revealthat the average of these flow rate were also lower than the average of the rest in the data set.


86

Hence, a possible explanation for this abnormality is problem with low LVN productindicating a possible cooling capacity limitation in the splitter distillation column.This PCA analysis is in fact an example of uncovering the source of hidden information in thedata, which can be use as guide for discovering the source of a potential problem in theprocess of a large plant.

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Isomerization, Loadings for PC# 1 versus PC# 2

Figure 4.19 : Loading for PC number 1 versus 2.


87

4.8 Conclusion

In this chapter, the essential steps in development of multivariate process model applyingchemometric approach is presented. The purpose is to describe how every single step isperformed in this work in order to provide a strong background for description of the modelspresented in chapter 5.

A general scope for chemometric model development and a procedure with its different stepsis presented and discussed in section 4.2. This procedure includes discussions of the objectiveof modeling, selection of variables, data collection and sampling, data treatment and scaling,selection of suitable method, calibration and validation of the obtained chemometric model. A more specific system definition and description of the process with different productionunits is presented in order to clarify the background and the motivation for the selected inputvariables to be used for the prediction models.In section 4.4, and 4.5 the description of output and input variables are presented. Thecalibration and validation data sets along with sample mean, variance, maximum and minimumvalues are presented for each variable in order to assess the data. The problem regarding sampling frequency is discussed in section 4.6. This discussion willserve as a background for the proposed solution discussed in chapter 5.A PCA model is developed for each catalytic reformer and isomerization unit. The PCAanalysis is performed in order to assess and classify the type of behaviours represented in thedata used for the developed models. The PCA analysis shows that there is a systematicvariation in data, indicating the existence of at least two different operation modes. The periodof operation in each mode is around a few days up to a few weeks. The results of PCAsuggests that the operation modes are related mainly to the desired quality of RON andbenzene contents rather than RVP. It is concluded that it is not appropriate to separate thesetwo regions, and a common model should be developed for the whole calibration data setcontaining 10 months operation data. The PCA analysis has also shown an abnormality in isomerization unit, indicating that aportion of the obtained data corresponding to 12% of total 13 months operation lies outsidethe 95% confidence interval. The analysis has shown that the operating temperatures in thereactors, along with the feed flow rate to isomerization and deisopentanizer unit were low inthose period of abnormality, suggesting a possible obstacle in operation of the splitter. Thedata for the period of abnormality is excluded from the calibration set and hence the obtainedmodel will be valid only for the normal operation.


88

Chapter 5

Models for Reformateand Isomerate Products

5.1 Introduction

5.1.1 Purpose

The purpose of this chapter is to describe structure, calibration, validation, and performance ofthe chemometric models developed for quality prediction of reformate and isomerate productsin gasoline processing area. The objective is to describe the basic principles in modeldevelopment, and to demonstrate how the problems are solved. In this chapter the developedmodels for prediction of RON, RVP, and aromate (benzene) contents of the product incatalytic reformer I are presented and discussed. The corresponding models for catalyticreformer II and isomerization unit can be found in appendix A and B since the basic steps andthe results of these model identifications are quite similar to those described in this chapter.

Chapter 5 Models for Reformate and Isomerate Products

89

5.1.2 Background

As it is described in chapter 2 and discussed further in chapter 4, there are a total of 9 differentblend components used in the gasoline blending unit. It is important to know the qualityvariables of all streams sent to the gasoline blender in order to optimize the quality of finalgasoline products. For some blend components, it is easy to estimate or calculate the qualities.For instance, three of the total nine blend components can be considered as almost purecomponents. These are oxygenate, butane and isopentane. Their qualities can be estimatedbased on pure component property. Regarding LVN and LVBN; i.e. light virgin naphtha andlight virgin visbroken naphtha, the qualities can be calculated or estimated since they containlight hydrocarbon components which can be identified by chromatographic analysis. However, for the reformate and isomerate products from catalytic reformers and theisomerization unit it is not possible to estimate or calculate the qualities easily due to thecomplex process of reforming and isomerization, and predictive models are needed.Furthermore, it is expensive to have on-line quality measurements for these three intermediateproducts in order to have the same sampling frequency as the other process variables. Theonly existing quality measurement for the reformate and isomerate streams are laboratoryanalyses, which are available only once per day, i.e. a sample interval of 24 hours, for eachquality. Input variables in these units are measured on-line, and a sample interval of one houris chosen for these variables in order to satisfy the demand for a sampling rate 4-10 timesfaster than the response of the system, as described in chapter 4.The output from the models are Research Octane Number (RON), Reid Vapor Pressure(RVP), and aromatic contents of the products (Benzene). The inputs are a set of selectedprocess variables. In order to fulfill the assumption of an informative input set as described inchapter 3, a set of inputs is selected based on general chemical engineering principles andknowledge of the process, in which the selected inputs are expected to have significant influence on the output variable. The inputs and output variables were presented and discussedin chapter 4.

The reformate and isomerate products from catalytic reformers and the isomerization unit areespecially interesting since they have high octane number and low aromatic characteristics.The gasoline blending process can be considered as a batch process in which the blendcomponents are used in order to produce the final gasoline products. The quality and volumeof the final products are fixed by the refinery production schedule. If there is no feedintroduced to the blendstock tanks during the period of blending, i.e. so called standing tanks,then the measured or predicted qualities of the blend components remain constant during theblending, and hence a Linear Programming (LP) approach in optimization of blending processwould be successful (Singh et al. 2000). The normal practice for the gasoline blending process in the refinery is that the qualitiy of thematerial in the blendstock tanks are measured once a day and used to estimate the first recipefor the blending process by using a LP optimization approach. The process is controlled byperforming feed-back control using on-line measurements of the qualities in the outlet streamof the gasoline blending.The blendstock tanks are supplied by continuous feed streams during the blending process, i.e.so called running tank. In this situation the assumption of constant quality of the blendcomponents is no longer valid and applying the LP formulation will not handle suchtime-varying feedstock qualities adequately. A solution for the blending problem is obtainedsince feed-back control is used based on on-line quality measurements of the product stream.


90

However, this solution will not be an optimal solution due the time-varying qualities of theblend stocks.The RON quality of the reformate streams is predicted using a multivariate regression methodsand then applying bias updating. The bias updating is based on the daily measurements ofRON reported by the laboratory and involves comparing the measured RON with thosepredicted by the model and then the difference is added as a constant in order to update themodel with the new measurement. In this approach it is assumed that the RON quality remainunchanged during the period of bias updating, which is not an appropriate assumption.The solution strategy proposed in this thesis is based on applying a moving horizonoptimization for the blending problem in which the quality variables are predicted based on thevariation of the upstream process and then provide the blending optimization problem with thepredicted previous, present and future qualities of blendstocks (Nikalou 1998, and Singh et al.2000).

In this chapter, the prediction models for the qualities of reformate and isomerate productssent to the blendstock tanks are presented and discussed.

5.1.3 Outline

In section 5.2 a discussion about selection of the methods applied for model development ispresented. In this section the proposed technique for handling the missing values of outputvariables are described.The models for prediction of the quality of the reformate product stream of catalytic reformerI, along with model development procedure, are presented and discussed in section 5.3. The conclusions for the quality prediction models are summarized in section 5.4


91

5.2 Selection of the Method

In chapter 3, the different methods in process chemometrics are discussed. These are staticand dynamic modeling methods in which both of them may use linear or nonlinear approachesin parameter estimation. All these type of modeling methods has been examined for predictionof the quality of reformate products. A great del of time has been spent on developing neuralnetwork models as a static nonlinear method, PLS as a static linear, and ARX as a time-serieslinear method.It has been found that the output signal exhibit correlation to the past values of input andoutput signals. As it is motivated by the discussion in chapter 4 regarding sample rate ofoutput signal, the best result has been found using the ARX identification method. Parameter estimation in an ARX model is conventionally performed by a Least Squares (LS)regression method, as it is suggested by Ljung (Ljung, 1987). Better result in this work isobtained by ARX model in which the parameters θ are estimated by a PLS model in analogywith the described relationship between a PCA and ARX model by Wise and Gallagher 1996.Applying a PLS method in parameter estimation of ARX model has increased the strength ofthe predictability by taking advantage of the ability of PLS method to extract the usefulinformation from collinear, noisy, input data which is relevant for modeling the output .The low sampling frequency for model output has given rise to a challenging problem in thiswork. A solution to this problem is proposed which is related to one of the following twosituations. If the output variation is slow moving from one day to the next day, as the case of RON, alinear interpolation of the output is performed in order to estimate the missing output values incalibration data set. However, applying interpolation is avoided in validation data set. Duringthe validation the model predicted output at time t is used to compute the output at time t+1.If there is a considerable variation in the output signal, indicating a possible faster dynamicduring a day, such as the case of prediction of RVP and aromatic contents, interpolation is notan appropriate approach in order to estimate the missing output. The solution here is that theinformation of the pervious outputs is imposed in the suitable structure of the ARX model.The structure of the ARX model is based on a form of regression vector in which the hourlysampled input variables are used together with the previous existing output measurement,normally measured at time t-24 hour, in order to model the output at time t. This solution isintegrated in the regression matrix of the ARX structure, in which the delay time for output isinherently 24 hours. In the following a review of the ARX model structure is presented:

A(q)y(t) = B(q)u(t) + e(t) (5.1)

A(q) = 1 + a1q−1 + ... + anaq−na

B(q) = b1q−1 + ... + bnbq−nb (5.2)

θ = [a1 a2 ... ana b1 b2 ... bnb ] (5.3)

ϕ(t) = [y(t − 1)....y(t − na) u(t − 1).... u(t − nb)]T (5.4)

y(t θ) = ϕT(t) θ (5.5)where: y(t) is output measurement at time t,u(t) is input measurement at time t,


92

e(t) vector of white noise sequences,q is the backward shift operator q-1 in which q-1 u(t) = u(t-1) na is number of A parameters,nb is number of B parameters,θ is the model parameters which include a and b parameters,φ(t) is the regression vector,

is prediction of new y at time t as a function of model parameters.y(t θ)

Following the terminology in ARX model, na and nb are defined as the number of A and Bparameters for previous output y and inputs u, respectively. The order of the ARX model isdefined to be the number of past input and output variables considered in the model. Furthermore, there may well be a delay from output to each of the input variables. Thesedelays are defined as a vector K of scalar value ki corresponding to delay for each input andoutput. Thus, nk would be the number of k delay parameters which is equal to number ofinput variables. Thus the standard ARX model may be written as equation 5.1, where inputs and outputs aresampled with the same sample interval. However for many quality variables the standardsampling procedure involves a nq =24-hours sampling interval, whereas the input variables areassumed known every hour. In order to use the available data for model development asuitable model representation must be developed. This is here accomplished based upon theARX model in equation 5.1. Since however the outputs between ....t-nq, t, t+nq.... areunknown, a model predict these values would be convenient for developing a predictor for thequality variables at their sampling times. The development of this predictor is here based on asimple first order predictor based upon the sampling interval for the input vector u(t):

y(t + 1) = ay(t) + bU(t − k) (5.6)

where k is the vector of input delays.The above model is used to predict the quality variable y(t+nq) as follows:

y(t + 2) = ay(t + 1) + bU(t − k + 1) = a2y(t) + abU(t − k) + bU(t − k + 1)y(t + 3) = ay(t + 2) + bU(t − k + 2) = a3y(t) + a2bU(t − k) + abU(t − k + 1) + bU(t − k + 2)

.

..

y(t + nq ) = anq y(t) + Σi=1

nq

a i−1 bU(t − k + nq − i)

Thus defining new parameters as follows:a1 = anq

andb i = a i−1b for i = 1, ..., nq (5.7)

the predictor may be written as:

y(t + nq ) = a1 y(t) + Σi=1

nq

b iU(t − k + nq − i)

= a1 y(t) + b1U(t − k + nq − 1) + b2U(t − k + nq − 2) + ... + bnq U(t − k) (5.8)


93

In this predictor the parameter values may be determined from plant data. It must be notedhowever that according to equation 5.7 there are only nu+1 unknown parameters, where nu isthe number of inputs in U(t-k). Since however the parameters in equation 5.8 are nonlinearlyinterdependent, it will be attempted to estimate all nu* nq+1 parameters in equation 5.8 using alinear parameter estimation method. To summarize, the above predictor is based upon a first order model in the input sample time.In the following presentation and discussion, the model order will be labeled one with respectto the output and the number of inputs included in the predictor should be nq according toequation 5.8. When applying equation 5.8 for modeling, it will be attempted to use nq numberof previous inputs. However if it becomes difficult to estimate all nu* nq input parameters oneshould apply a nonlinear parameter estimation method to determine the a and b parametersdirectly. The derivation of the first order predictor in equation 5.8 was based on a first order model inthe input sample time. A higher order model might also be used, which would lead to usage ofolder quality variable measurements, which means that y(t-24) and y(t) would be used topredict . Such a model would lead to an even higher number of parameters to bey(t + 24)estimated using a linear estimation method. For higher order models initialization alsobecomes an issue.

It is noteworthy to mention here that we start with a number of nb equal to 24 in order toassure that all existing variation in input variables is included. It is important for thepredictability and quality of the model that the existing dynamic variation in input which ismost relevant for modeling of output is covered. Thus, the choice of nb=24 seems to be mostappropriated. However, choosing number of nb equal to 24 has a disadvantage that thenumber of model parameters will become high. These issues will be discussed further in calibration and validation of the RVP model in section5.3.2. Hence, the parameter nb, i.e. the number of input vector, is assumed unknown for thetime being and must be determined during the model development. In this work when we talkabout the number of input vector, we actually mean only the number of past input variables toconsider, i.e. number of nb, since we have a fixed number of na equal to one. The regression vector in equation 5.4 is used in the objective function in the LS method, inwhich it is minimized with respect to θ, in order to find the best fit, as it is discussed in chapter3. The regression vector can be expressed as follows:

ϕ(24) = [y0 U23 U22 U21 ..........U24−nb]ϕ(48) = [y24 U47 U46 U45 ...........U48−nb]

...

...ϕ(N) = [yN−24 UN−1 UN−2 UN−3 ...........UN−24−nb]

(5.9)

where N refer to number of existing output variable. It is assumed that the delay parameter k is equal to one in equation 5.9. All the regressionvectors in equation 5.9 are used to form a regression matrix, which is used in a PLS regressionmodel in order to estimate the model parameters θ defined in equation 5.3. An example of how the regression vector is built for this application is shown in table 5.1. Thethree columns in table 5.1 represent respectively time in hours, output y and input U. Letassume that the starting time is t0, and then y0 and U0 is the corresponding output and inputsat time 0. The first predicted output in this formulation would be y24.


94

Thus, the regression vector used for prediction of y24 contains the previous output, i.e. y0,and also all the previous values of U inputs, from U23 and backward corresponding to thedetermined model order, i.e. nb, and the delay k. The same procedure is used to form theregression vector corresponding to prediction of y48.Determination of the nb parameter will lead to the number of the previous inputs considered inthe model, which is shown by gray area in table 5.1. It is assumed that the delay parameter k isequal to one in table 5.1.

T Y U

0 y0 U0

1 U1

2 U2

.. ..

.. ..

.. ..

21 U21

22 U22

23 U23

24 y24 U24

25 U25

26 U26

.. ..

.. ..

45 U45

46 U46

47 U47

48 y48 U48

49 U49

50 U50

.. ..

.. ..

Table 5.1 : The structure of regression vector with delay k=1.

The software used in this work is MATLAB for windows, The MathWorks, Inc., version4.2c.1, 1994. For ARX and PLS model development the Identification Toolbox of Matlab,and a university version of the PLS-Toolbox version 1.5.1, 1995 by B.M. Wise, as well as theroutine developed by the author of this thesis are used.


95

5.3 Models for Catalytic Reformer I

5.3.1 Introduction

In this section the models for prediction of RON, RVP, and benzene contents of reformateproduction from catalytic reformer I will be presented and discussed. The input variables used for the models are described in chapter 4, along with a detailedPrincipal Component Analysis (PCA), and a description of data treatment.In the following sub-sections, there will be more focus on model structure, calibration,validation, and performance of the models.

5.3.2 RVP Model

5.3.2.1 Inputs and Output

The selection of input variables relies basically on general knowledge of the process and anassessment of which variable have the largest effect on the output. The principles in selectionof input variables in order to obtain a set of informative input data are discussed in chapter 3.If a model is sensitive to one or more input variables meaning that those variables have a largeinfluence on the predicted output, then the corresponding parameter values will be largecompared to the other parameters. This concept is used in model development by using all candidate input variables in thebeginning and then after validation the non sensitive variables are excluded from the inputs.The advantage of this procedure is to prevent exclusion of those variables that can beinfluential on the output prediction due to a multivariable effect or existence of an unknownphenomena. In this section an example of this procedure is presented. The following input variables areused in the RVP model as the initial selected variables.

1 Mole H2/ Mole C in recycle gas2 % H2 purity in recycle gas 3 Reactor 1 outlet temperature4 Reactor 2 outlet temperature5 Reactor 3 outlet temperature6 Reformer Feed flow rate7 C-401 Reformate flow rate8 C-401 Liquid gas flow rate9 C-401 Reflux flow rate10 C-401 Feed temperature11 C-401 Reboiler temperature12 C-203 Reflux flow rate13 C-201 Naphtha side stream temperature (Pressure Corrected)14 C-601 Naphtha side stream temperature (Pressure Corrected)15 C-203 Bottom temperature (Pressure Corrected)16 C-652 Bottom temperature (Pressure Corrected)


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It will be shown that for the final model variables number 7 through 12 will have the largesteffect among all variables, as it is expected.The output is RVP measured by laboratory. Thus, the mode will be a Multi Input SingleOutput (MISO) case.

The calibration data set is chosen from a period of approximately 9 months operation startingfrom October 1. 1996 to June 13. 1997. The validation data cover approximately the rest of1997, i.e. June 13. 1997 to December 30. 1997. There are some days, both i calibration andvalidation, where both input and output data are missing. These missing datas are mainly dueto operation shutdowns. Besides, there are also some missing data for a few hours because ofproblems in data acquisition system or sensor faults.

5.3.2.2 Model Structure

As mentioned earlier, the model structure is based on an ARX model in which the parametersθ are estimated by a PLS model. Based on the discussion in section 5.2, we will take only theeffect of y(t-24) for output, as in equation 5.8, and hence we will have only one A parameter.Regarding the B parameters we are seeking for as much effect from the inputs, and hence theB parameters will be as many as necessary to get an acceptable low prediction error and asatisfactory model performance, as it is discussed in the following. We are specially interestedto examin the case of nb=24, as it is discussed in the following section.In parameter estimation we use a PLS model in which we need to determine a suitable numberof principal components PC. The number of PC is also called number of Latent Variables(LV).Thus, there are two parameters in model development, i.e. nb and the number of LV, whichhave to be found. This task is handled by developing a recursive routine in Matlab, in which the Root Mean SumSquares Error in Validation (RMSSEV) is used as the criterion for optimization of nb andnumber of PC. RMSSEV is defined as the following.

RMSSEV =Σi=1

n

(y i − y i)2

n (5.10)

where is the model predicted output and yi is the measurement for all data over time t.y i

Notice that we have only one output and n is the total number of y. The results for thesesimulation are described in the next subsection.

5.3.2.3 Identification

As mentioned before, the purpose of calibration is to estimate the optimum values for themodel parameters θ, along with nb, and the delay parameter k for each input variables. Noticethat na is one in our case. The purpose of the validation is, however, to evaluate the modelobtained in the calibration. Since the model has time-series dynamic characteristic, it isimportant to secure a calibration and validation set containing time sequence of subsequentdata. For that reason, it is not desirable to mix the data and select a random test set data forvalidation. Furthermore, based on process knowledge it is known that the operation mode isdifferent in summer and winter seasons. Thus, the validation is performed applying a


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completely distinct set of data, and it is attempted to cover both winter and summer operationmode both in the validation and calibration data sets. Calibration and validation of the obtained models are inherently related, and the models areevaluated based on some criteria concering both calibration and validation phases, as we shallsee in the following sections.

5.3.2.3.1 ARX Model With All Inputs

Referring to the developed model structure defined in equation 5.8, it is especially interestingto study the case of nb=24, in which the effect of inputs is covered all the way back to y(t-24).This case is discussed in this section. Nevertheless, as we shall see in the next section, it will be shown that special cases exist inwhich the number of model parameters can be reduced with no significant loss of predictionability. Number of delay parameter in this case is k=1 for all input variables, since it is desired to takethe effect of all previous input values on the prediction of output, even if the effect is small.One parameter remaines to be estimated, and that is number of latent variables LV. Figure 5.1shows the result of a series of recursive simulations, in which RMSSEV is calculated as afunction of LV.

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Number of LV

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Figure 5.1 : RVP Model, RMSSEV as a function of LV for nb =24, and delay K=1.

It can be seen in figure 5.1, there are three local minima around LV equal to 4, 7, and 15.Choosing more LV will result in increasing total number of model parameter, which will causeover fitting, as discussed in chapter 3. As we shall see in the next section, where we discuss the optimum number of LV, we willchoose a number of LV = 6. Notice that with LV=6 a RMSSEV=2.65 is obtained, which isnot far from the local minimum RMSSEV=2.5 at LV=15.


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Another reason for choosing LV=6 is that the results of the case nb=24 presented in thissection, is desired to be comparable with the results that will be presented in the next section.

Consequently, calibration of the model is performed, and the model parameters θ areestimated by choosing LV=6, delay parameter for all inputs equal to one, na =1, and nb=24.Notice that by having 16 inputs, we will get a total number of 385 parameters in the θ vector,according to equation 5.3. Table 5.2 shows the percent variance captured by PLS model. As it can be seen, the capturedvariance in X-block, i.e. inputs, and Y-block, i.e. output, are respectively 75.99% and 50.35%.

Percent Variance Captured by PLS Model

X-Block Y-Block

LV # This LV Total This LV Total

1 30.17 30.17 18.08 18.08

2 21.92 52.09 8.52 26.60

3 3.34 55.43 16.85 43.45

4 5.56 60.99 3.37 46.82

5 4.96 65.95 2.77 49.58

6 10.04 75.99 0.76 50.35

Table 5.2 : RVP model, percent variance captured by PLS model.

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Figure 5.2 : RVP Model, prediction error in validation, nb=24, delay K=1.

Figure 5.2 shows the prediction error in validation. Notice that the error is the differencebetween the model predicted and the measured RVP and it has the pressure unit. i.e. kPa.Recal the measureed RVP data for catalytic reformer I in table 4.2 in chapter 4, in which the


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average RVP is 49.67 kPa, and the standard deviation is 3.02 in calibration data. We shall latercompare these data with the results presented in table 5.3. The corresponding prediction errorin calibration is shown in figure 5.4.

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Figure 5.4 : RVP model, prediction error in calibration, nb=24, delay K=1.


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Figure 5.3 shows a histogram plot of prediction error in validation. This plot will give us animpression of how close the error signal is to a normal distributed zero mean noise. Thecorresponding histogram polt for calibration is shown in figure 5.5.

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Figure 5.5 : RVP model, histogram plot of prediction error in calibration.

As it is described in chapter 3, in order to evaluate the performance of the model the RMSSEis compared with a reference obtained from either a zero-model or an average-model. The average reference model is computed by first calculating the average of all N measuredoutput values, and then subtract the average from the output itself to calculate EAVG , asfollows:

(EAVG) i = y(t i) − yAVG (5.11)

Then, we compute a RMSS of this error by using equation 5.10, and denote it as RMSEAVG.It is clear that the RMSEAVG has the same property as the standard deviation of themeasured output. We expect that the developed prediction model should predict a set ofoutput values for a period of time which is closer to the measured output than the averagevalue. In this sense we say that the developed model should be at least better than the averagevalue model in order to be accepted.A second reference model is defined based on the following consideration. Consider a modelstructure as given in equation 5.8 in which the number of A-parameter is 1, i.e. na=1.Furthermore, consider that the developed prediction model find a set of B-parameters which isclose to zero, and an A-parameter value close to one This is shown in the following equation:

y(t) = y(t − 24) + 0 (5.12)

This means that the new prediction of y is equal to the previous measured y. In this case wehave no effect of input variables and the model just predicts the next output equal to the


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previous measured one. Based on this consideration, we compute a EZERO in a general form asfollows:

EZERO = y(t i) − y(t i+1) (5.13)

Hence, a RMSS of EZERO , which is denoted by RMSEZRO will give us a reference inassessment of predictability of the obtained prediction model. Thus, the expectation is that amodel with good performance characteristics should be better than the zero-model, meaningthat the developed model has captured the effect of input variables.Table 5.3 shows RMSSE in both calibration and validation along with the average-model andzero-model in this RVP model.

Validation Calibration

RMSSEV 2.65 RMSSEC 2.05

RMSEAVGV 3.28 RMSEAVGC 2.91

RMSEZROV 4.10 RMSEZROC 3.05

Table 5.3 : RVP model, RMSSE, average-model, and zero-model in validation and calibration.

It can be seen that the RMSSEV is less than average- and zero-model, indicating that themodel has captured essential variation both in input and output.

Another way to evaluate the model performance is a so called open-loop simulation of themodel. In this simulation the predicted output at time t is applied instead of measured outputin order to predict the next output value at time t+1. This model simulation is performed aftermodel calibration. We shall call this simulation as open-loop simulation in which the newpredicted value is used instead of the measured output for prediction of the next output value.Open-loop simulation will show the predictability of the model during a period of operationwithout having the actual output measurement. It is interesting to see the open-loop simulation in both calibration and validation for RVPmodel. These are shown in figure 5.6 and 5.7 respectively

In Figure 5.8 a plot of predicted versus measured RVP in calibration is shown. These plotshows how successful the calibration is performed. However, it is more interesting to studythis plot in the validation case. The corresponding plot for the validation can be seen in figure5.9. As it can be seen the model has captured the essential variation of RVP with a RMSSEVof 2.65.

The results obtained in this section will be discussed later in the next section, where possibilityof reducing the number of model parameters will be discusssed.


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Figure 5.6 : RVP Model, Open Loop Simulation in calibration

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62RVP LAB, Validation, Open Loop Simulation

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Figure 5.7 : RVP Model, open loop simulation in validation


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Figure 5.8 : RVP model predicted versus RVP measured in calibration.

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Figure 5.9 : RVP model predicted versus RVP measured in validation


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5.3.2.3.2 Reducing the Number of Model Parameters

As it is mentioned in the previous section, a number of nb equal to 24 would be logical inorder to cover the variation of input, since the predictor in eqution 5.8 contains y(t-24). Thedisadvantage of choosing nb=24 is the high number of model parameters, which may cause anover fitting problem. However the validation results in table 5.3 and figue 5.9 do not indicateproblems with overfitting. In this section, it is attempted to reduce and find the optimum number of model parameters,with no significant loss of predictability. Apart from number of input vectors nb and number of LV, one more parameter has to bedetermined, which is the delay for each variables as expressed in equation 5.8.One way to find the number of delay parameters is to perform calculation of residence time intanks, vessels, units and pipeline. Moreover, if a first principles mathematical model wasavailable, the effect of variables in energy balance, such as reactor outlet temperature could beinvestigated. Another way is to let the model find the delay parameters. This can be done by a series ofrecursive simulations in which the best set of delay parameters are found giving the minimumRMSSEV defined in 5.10. In this work, these two approaches are combined in which the search for delay parameters islimited by some qualified estimate according to process knowledge and physical restrictions,such as the length of the pipeline, the volume of tanks and etc, and then let the model find thebest delay parameters.

The search for the optimal ARX model order for input variables, i. e. nb, and number of LV iscarried out by a series of simulations, in which nb and LV are changed from 1 to 25 for nb,and from 1 to 33 for the number of latent variables (LV). The choice for maximum number ofLV is based on the following considerations.Number of LV is a function of number of variables, and ARX order, as shown in equation5.14.

Max. LV = na ⋅ ny + nb ⋅ nu (5.14)

where ny is the number of output, and nu is the number inputs variables.

Since we have na = 1 and ny = 1, the product of na and ny is equal to one. Notice that wehave 16 input variables, and hence the maximum number of LV will be 17 and 33 forrespectively nb = 1 and nb = 2: Max. LV = 17 for nb = 1 Max. LV = 33 for nb = 2

Selecting more LV has two disadvantages. First, choosing more LV means adding more noiseto the structure part, and second, total number of model parameters will increase and it willcause overfitting, as it is discussed in chapter 3.For that reason, a maximum of 33 number of LV has been chosen in this investigation fornumber of nb larger than 2.


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Figure 5.10 shows the calculated RMSSEV as a function of nb and LV, for nb from 2 to 25and LV from 1 to 33. The plot for nb=1 is shown separately in figure 5.13 since maximum ofLV is 17 according to equation 5.14.It can be seen that there is a region of nb less than 5-7 that RMSSE has its minimum.Moreover, RMSSEV increases in the region of LV larger than 15-17 due to additional noise inthe structure part.In table 5.4, the minimum RMSSEV is shown for each nb, along with number of LV at theminimum. The percent variance captured by PLS model is also shown both for input(X-Block) and for output (Y-block). As we can see in table 5.4, the minimum RMSSEV isfound for nb = 2 and LV = 23 at a value of 1.89. Besides, as it is shown in figure 5.10 anotherlocal minimum appear to be around nb=7.The next job is now to study the progress of RMSSEV for some nb parameters in more detail,and eventually obtain a model with fewer parameters, with no significant loss of predictionability.

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Figure 5.10 : RVP Model, RMSSEV as a function of nb and LV.

Figure 5.11 shows the RMSSEV for nb=1, which we could not see in figure 5.10. Figure 5.12shows the RMSSEV for nb=2. As it can be seen in these two diagrams a local minimumappear at LV around 5-6 and then another minimum RMSSEV at 17 and 23 number of LVrespectively.Furthermore, it can be seen that the value of RMSSEV is around 2.2 for nb=2 and LV=6,which is actually the first local minimum. It seems that this case is more preferable rather thanthe case with nb=2 and LV=23 since the total number of model parameters is smaller and thedifference between the two RMSSEV is not too large.


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0 5 10 15 201.5

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Number of LV

RM

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Figure 5.11 : RVP Model, RMSSEV as a function of LV for nb =1.

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Number of LV

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nb Min.RMSSEV

X-Block Y-Block LV

1 1.96 99.99 43.86 17

2 1.89 99.94 47.69 23

3 2.02 97.88 48.39 15

4 2.16 83.57 44.00 7

5 2.13 93.60 48.41 11

6 2.13 98.55 55.05 21

7 2.03 97.56 55.84 19

8 2.13 97.25 57.05 19

9 2.18 94.13 53.46 13

10 2.22 94.45 55.08 14

11 2.18 94.23 55.91 14

12 2.27 93.98 57.24 14

13 2.26 96.35 63.40 19

14 2.41 96.08 66.05 19

15 2.41 95.91 66.13 19

16 2.46 94.91 64.64 17

17 2.49 62.18 44.55 4

18 2.51 61.92 44.52 4

19 2.54 95.16 70.38 20

20 2.54 95.21 72.66 21

21 2.51 94.44 72.03 20

22 2.47 94.44 71.92 20

23 2.46 93.52 69.27 18

24 2.44 93.78 70.68 19

25 2.43 93.54 70.92 19

Table 5.4 : RVP model, Minimum RMSSEV for different nb, and LV.

As mentioned earlier, another local minimum appear to be around nb=7. Figure 5.13 showsthe RMSSEV for nb= 7. A comparison of between this diagram and figure 5.12 shows that theobtained RMSSEV in the case of nb=2 and LV=6 is still preferable, since both the value ofRMSSEV and the model order is smaller in the latter case. Selecting the best nb and LV is of course based on performance of the obtained model invalidation. The important issue is to capture the maximum effect of input variables inprediction of output, and obtain a model which has an acceptable general characteristic. Asmentioned previously, it is important to selcect one of the best models with fewer modelparameters among a set of model candidate .In all phases of model development procedure from determination of optimal delay parametersto calibration of the model along with determining optimum number of LV and nb, validationis an essential part of the development work.


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In the following the result in calibration and validation of the selected model with nb=2 andLV = 6 will be presented.

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The order of the ARX model is thus as follows: na = 1, and nb = 2.The following delay parameters has been found for each input variables, using a series ofrecursive simulation:

K = [2 2 3 3 3 2 1 4 2 2 1 4 17 17 5 10]

It is interesting to see the progress of PLS regression. Table 5.5 shows the percent variancecaptured by PLS model. As we can see the captured variance in X-block, i.e. inputs, andY-block, i.e. output, are respectively 77.34% and 43.63%.

Percent Variance Captured by PLS Model

X-Block Y-Block

LV # This LV Total This LV Total

1 26.02 26.02 24.58 24.58

2 27.98 54.01 6.09 30.67

3 4.34 58.34 9.00 39.67

4 4.65 62.99 2.17 41.84

5 8.35 71.34 0.97 42.81

6 6.00 77.34 0.82 43.63

Table 5.5 : RVP model, percent variance captured by PLS model.


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The first thing we are interested in to examine is the level of prediction error in bothcalibration and validation. Figure 5.14 shows the prediction error for validation. Notice thatthe error here is the difference between model output and RVP measured in the laboratory,and the error value is not calculated based on autoscaled data, but it has the real unit, i.e. kPa.If we could obtain a perfect model, then we would expect that the error signal would haveapproximately the same characteristic as white noise. Thus, a histogram plot of the predictionerror will give an impression of how close the error signal is to a normal distributed zero meannoise. The histogram plot of error signal in validation is shown in figure 5.15.

Examining the same plots in calibration, would give os an impression of how well thecalibration is performed. If the prediction error in calibration is very small and much closer tozero than in the validation, it could be a sign of an overfitted model or perhaps the validationand calibration data are different and possibly from two different regions of operation. Figure5.16 and 5.17 show the respective plots of prediction error and histogram of error incalibration.

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Figure 5.14 : RVP Model, prediction error in validation.


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Figure 5.15 : RVP model, histogram plot of prediction error in validation.

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Figure 5.16 : RVP model, prediction error in calibration.


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Figure 5.17 : RVP model, histogram plot of prediction error in calibration.

Table 5.6 shows RMSSE in both calibration and validation along with the average-model andzero-model in RVP model. The development of zero-model and average-model are discussedin the previous section.





Table 5.6 : RVP model, RMSSE, average-model, and zero-model in validation and calibration.

It can be seen that the RMSSEV is less than average- and zero-model, indicating that themodel has captured the essential variation both in input and output.

The open-loop simulation in both calibration and validation for RVP model are shown infigure 5.18 and 5.19 respectively.In open-loop simulation predicted output at time t is used instead of measured output in orderto predict the output value at time t+1. Open-loop simulation will show the predictability ofthe model during a period of operation without having the actual output measurement.


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Figure 5.18 : RVP model, open loop simulation in calibration

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Figure 5.19 : RVP model, open loop simulation in validation

As we can see the model has captured the essential variation and follow the variation of RVPop and down, indicating a good performance.


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In the following the results the model simulation is presented when the measured output isused in the model for prediction of the next output. This model simulation is performed usingboth calibration and validation data set. Simulation of the model applying the same data setwhich is used for calibration seems superfluous. However, it will give an impression of howwell the calibration is performed. The expectation is that the model is capable to reproducethe calibration satisfactory.

Figure 5.20 shows the result of prediction of RVP in calibration in which the outputmeasurement is plotted versus model predicted RVP. It can be seen how well predictionfollows the measured output. Notice that RVPLAB is RVP measured at laboratory, andRVPMODEL is the predicted output.This result demonstrates that the model has captured the essential variation but there are somepoints that the model has difficulty to fit, mostly low RVP measurements.

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Figure 5.20 : RVP model predicted versus RVP measured in calibration

As we can see in figure 5.20, most of the points are lying around the diagonal line indicatingthat there is virtually no bias in the model except for some points that are slightly away fromthe diagonal line.

Figure 5.21 and presents the same simulation using validation data set. It shows RVP modelpredicted versus RVP measured in validation. It can be seen clearly that the predicted valuesfollow the variation of the measured outputs and demonstrate a good predictabilitycharacteristic.


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Figure 5.21 : RVP predicted versus RVP measured in validation

As it is discussed in chapter 3, in linear PLS it is assumed that the scores in the output Y-blockis a linear function of scores in input X-block, as it is expressed in equation 5.15.

u = b t + h (5.15)

b is called the inner relationship, or internal regression coefficients. A plot of score u versus score t can be useful in order to visualize and examine thefunctionality of u=f(t).For the RVP model this plot can be seen in figure 5.22 for the first u vs. the first t. As it can beseen from figure 5.22, there is no obvious nonlinear relationship between t and u, and thus thisjustify the use of linear PLS. In fact, nonlinear PLS has been investigate by the author. A number of simulations has beencarried out using both neural network and different degree of nonlinear polynomials. Theresults show no significant improvement by using nonlinear PLS in the RVP model.

The last step in assessment of model validation is to examine the model parameters andevaluate the sign and quantity of parameters in order to interpret the physical sense of theparameters.


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Figure 5.22 : RVP model, scores u1 as a function of scores t1.

As it is mentioned in the beginning of this section, the objective is to give an example of thegeneral procedure in model development, in which the performance of the developed model isevaluated and the model is accepted if the results indicate satisfactory prediction ability. Examining the model parameters at this point has shown that the developed model is notsensitive to some variables in which the respective parameter values are small.These variables are excluded from the inputs, and hence the whole procedure is repeated. Ithas been found that the following input variables have the largest effect on RVP output.

1 Reformer Feed flow rate2 C-401 Reformate flow rate3 C-401 Liquid gas flow rate4 C-401 Reflux flow rate5 C-401 Feed temperature6 C-401 Reboiler temperature7 C-203 Reflux flow rate

The obtained B-parameters are shown in table 5.7. There is only one A-parameter which is: a = 0.160.

The largest effect stem from variables number 2, 3, and 6, which are the variables chosenfrom the stabilizer column in catalytic reformer I shown in figure 4.3 in chapter 4.

The negative effect of variables 3 and 6 are correct since an increment in both reboilertemperature and liquid gas flow rate, which is the top distillate flow rate, will decrease RVP asa result of removing more light hydrocarbon components from the reformate product.


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Variable number 2 is the feed flow rate of reformate product itself. It has positive effectbecause more bottom product in the stabilizer means less top distillate, and hence more lightcomponent in the reformate.Variable number 4 is reflux flow rate in the stabilizer column. An increment in reflux flow ratemeans less distillate product and more liquid down-stream at the top of the column. It haspositive effect, meaning more light hydrocarbon components will be sent down through thestabilizer column, to prevent flooding at the top, which eventually end in the reformateproduct.

Variables Coef.foru(t-1)

Coef. foru(t-2)

Sign Description

1 0.101 0.103 + Reformer Feed flow rate

2 0.234 0.230 + C-401 Reformate flow rate

3 -0.233 -0.216 - C-401 Liquid gas flow rate

4 0.101 0.084 + C-401 Reflux flow rate

5 -0.055 -0.141 - C-401 Feed temperature

6 -0.261 -0.276 - C-401 Reboiler temp.

7 -0.030 -0.053 - C-203 Reflux flow rate

Table 5.7 : RVP model, B- parameters in ARX model.

Variable number 5 is the temperature of the feed to the stabilizer column. This temperaturerepresent the magnitude of the enthalpy introduced to the column, and hence has the sameeffect as reboiler temperature, i.e. sending more light hydrocarbon components upward andthus decreasing RVP. Variable number 1 is feed flow rate to catalytic reformer. In the first place, it is expected thatthe sign of parameter relating to this variable should be negative for the reason that the higherflow rate will increase the heavy components, since the feed to the catalytic reformer is HeavyVirgin Naphtha (HVN). It is difficult to say anything in more detail about the sign of thisparameter because of the complex reactions take place in the reactors. The positive sign canbe just an indication of promotion of cracking reactions and formation of more lighthydrocarbon components. Variable number 7, which has the smallest effect, is the reflux flow rate in the naphtha splitter.The main objective of the splitter is to split naphtha into LVN and HVN. Increment in thisreflux flow rate means more light components toward LVN and more heavy component toHVN, and thereby that a negative effect on RVP.


117

5.3.2.4 Discussion of Full ARX Model versus Reduced Parameters

In the previous two sections the results of two RVP models are presented. One model withnb=24 and delay parameters K=1, and another with reduced nb and optimum number of delayparameters K. Based on the developed structure of the ARX model presented in equation 5.8, in which wetake the previous existing output y, it is important that the model cover all existing dynamicvariation of input which is most relevant for modeling of output. Thus, the choice of nb=24seems to be most appropriated. On the other hand, there will be a risk of over fitting problem by applying nb=24, since itresults in a high number of model parameters. By the results presented in the previoussections, it is shown that the number of nb can be reduced with less significant loss ofpredictability by applying a set of optimum delay parameters K and LV. It has been shown thatnb can be reduced to 2, and at the same time keep almost the same level of predictability.However, the developed model with the reduced model order is a special case of the modelwith nb=24 and depends much on the condition that data has been obtained from. Dynamic variation of the input variables has a significant effect on the general predictability ofthe obtained model. Figure 5.23 and 5.24 show examples of variation of two important inputsused in modeling of RVP during one week of operation. Examining the variation of the inputsalong the whole period of the calibration and validation shows that there are significant lowfrequency changes in the characteristics of the variation in the different periods, presumablybased on the changes in the operation points related to the different seasons. Thus, applyingnb=2 may not be optimal, and there will be risk of loosing the general predictabilitycharacteristic.The conclusion is the model with nb=24 is the basic recommendable model, and the reducedmodel is a special case of the basic model, which only can predict low frequency changes ininputs.

0 50 100 150 20041

42

43

44

45

46

47

48Validation, Input no. 7, C-401 Reformate flow rate

Sample

m3

/hr

Figure 5.23 : RVP model, one week data for reformate flow rate.


118

0 50 100 150 2004.4

4.6

4.8

5

5.2

5.4

5.6

5.8

6

6.2Validation, Input no. 8, C-401 Liquid gas flow rate

Sample

m3/

hr

Figure 5.24 : RVP model, one week data for liquid gas flow rate.


119

5.3.3 RON Model

Research Octane Number RON is an important quality variable and has a tremendous profiteffect on the economy of the refinery. It is quite possible to use MTBE in order to compensatefor low octane quality in some gasoline products. However, this solution is expensive due tohigh price of the MTBE. Moreover, there is a maximum limit on the oxygenate contents ingasoline products due to environmental regulation and restrictions in different countries inEurope. These are two main reasons that make using oxygenate not a feasible solution forcompensating RON quality. The purpose of large investment on catalytic reformer and isomerization units is justified byachieving high octane number of gasoline products. By this it is possible to meet the marketdemands on octane quality and at the same time produce more environment friendly products.This is the strong motivation for control of RON quality in catalytic reformer in order to meetthe demands for production specifications and economy. However, the close-loop control ofRON has caused a difficulty in input-output modeling and prediction of RON quality, as it isdiscussed in chapter 3.


The following variables are chosen as the input variables in the RON model. These are thevariables expected to be most influential on the output RON.

1 Mole H2/ Mole C in recycle gas2 % H2 purity in recycle gas 3 Reactor 1 outlet temperature4 Reactor 2 outlet temperature5 Reactor 3 outlet temperature6 Reformer Feed flow rate7 Reformate flow rate

The total amount of input data is 5600, and 4334 in the calibration and validation data sets respectively. These data sets correspond to 9 months of operation data in calibration and 6months operation data in validation. Notice that the data corresponding to the periods ofprocess shutdown and outliers has been omitted. Regarding the output RON, there are only232 and 164 laboratory measurement available in respectively for calibration and validationperiods.


The control strategy of the reformer unit is based on close-loop control of RON quality due tothe great importance of octane number on production economy. The control action haseffectively resulted in small variation in output RON, as it is shown in table 5.8. The average,standard deviation, maximum, and minimum values for RON and the reactors outlettemperature are shown in table 5.8. It can be seen that the variation of RON and thetemperatures are small due to the small values of the standard deviations. Notice that the datain table 5.8 are calculated based on the calibration data set that covers 9 months of operation.


120

It has been found that the type of model structure used in the case of RVP model is notsuitable and effective for prediction of RON. As it is shown in chapter 4, there is morevariation in RVP than in RON.

Calibration Reactor Outlet Temperarture

RON R1 R2 R3

Average 99.97 430.92 471.10 500.33

Std. Deviation 0.37 4.21 4.62 3.54

Maximum 101.60 442.45 482.62 507.32

Minimum 98.60 421.67 460.40 489.89

Table 5.8 : Calibration data set, RON and reactor outlet temperatures

To overcome the problem of missing output value, linear interpolation is preferred betweenthe existing RON values, which is consequently based on the assumption that the variation ofRON from one day to another is small enough to permit a rough estimation of RON betweentwo subsequent existing RON measurement by interpolation. Since interpolation is applied inorder to estimate the missing RON output, an equal number of observations in both input andoutput data set is thus obtained.

The model structure is based on an ARX model of the general type:

A(q)y(t) = B(q)u(t) + e(t)

in which the parameters are estimated by a PLS regression. The number of A-parameter, andB-parameters, are determined by model order, and we will have the same number of na, andnb. It is very important to emphasize that the interpolation is performed only in calibration dataset. In the validation, we let the model apply its own predicted output in order to predict thenext output.

5.3.3.3 Calibration

As it is described in the case of RVP model, a set of suitable delay parameters, optimal modelorder and number of LV parameter need to be determined. These parameters has been foundby numerous recursive simulations. The following delay parameters has been found for the input variables:

K = [16 16 18 18 18 4 7 ]

There is no delay for output RON.

Table 5.9 shows the values of RMSSV obtained for the different ARX orders and LV, inwhich the model order is changed from 1 to 20 in order to search for all possible effect ofvariables up to t-24, i.e. the previous measured RON. The maximum number of LV is afunction of model order.


121

ARXOrder

Min.RMSSEV

X-Block Y-Block LV

1 0.896 12.78 83.46 1

2 0.111 97.26 99.29 4

3 0.104 97.91 99.48 4

4 0.116 99.11 99.58 4

5 0.042 99.02 99.60 14

6 0.040 99.28 99.61 14

7 0.053 97.39 99.42 13

8 0.053 98.07 99.47 16

9 0.052 97.83 99.45 16

10 0.055 97.59 99.44 16

11 0.056 95.78 99.11 12

12 0.057 98.12 99.54 21

13 0.050 97.98 99.53 21

14 0.048 97.87 99.51 21

15 0.050 97.92 99.52 22

16 0.054 97.83 99.51 22

17 0.054 97.71 99.51 22

18 0.055 97.72 99.54 23

19 0.050 97.61 99.53 23

20 0.050 97.50 99.52 23

Table 5.9 : RON model, min. RMSSEV for different value of ARX order and LV.





Table 5.10 : RMSSE, average-model, and zero-model in validation and calibration

Table 5.10 shows the obtained RMSSE in calibration and validation along with the values ofRMSSE for the average-model and the zero-model respectively. It can be seen in table 5.9 thatalready by a third order ARX model, the value of RMSSEV reaches a first local minimum at is0.104 and a comparison with the reference models in table 5.10 shows this value can beaccepted.It is important to notice again that these RMSSEV values are calculated based on that themodel apply its own predicted output in order to predict the next output.Based on the these results, it is concluded that a third order model with LV=4 can be anappropriate candidate for the accepted model considering the discussion about fewer modelparameters in order to avoid overfitting.


122

Hence, the model structure of ARX order=3 , and LV = 4 is chosen. That means we will get 3a-parameters, and 21 b-parameters corresponding to 7 input variables.

0 50 100 150 200 250-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15Error in Calibration

Figure 5.25: RON model, prediction error in calibration.

0 50 100 150 200 25098.5

99

99.5

100

100.5

101

101.5

102RON, Calibration, Open Loop Simulation, OR=3, LV = 4

Sample

RO

N S

imul

ated

(o) a

nd R

ON

LA

B(*

)

Figure 5.26: RON model, open loop simulation in calibration.

The prediction error in calibration is shown in figure 5.25. Notice that the obtained RMSSE incalibration is 0.054. The calibration data consists of 5600 input-output data, in which only 232of them are measured RON by laboratory and the rest is estimated by linear interpolation. In


123

figure 5.25, only the error corresponding to existing measured RON is shown, and the errorcorresponding to interpolated data is omitted.Figure 5.26 shows the so called open-loop simulation of the model in calibration, in which thenew predicted value is used instead of the measurement for prediction of the next outputvalue. The open loop simulation indicate that the calibration is satisfactory.Figure 5.27 shows a histogram plot of error in calibration, which exhibits an approximate zeromean error.

-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.150

5

10

15

XBIN

BIN

Error in Calibration

Figure 5.27: RON model, histogram plot for prediction error in calibration.

5.3.3.4 Validation

The validation is performed applying a completely distinct set of data. As mentioned beforethe input data in validation set consists of 4334 number of data covering 6 months ofoperation. In this period, after omitting the outliers, there are only 164 laboratorymeasurements of output RON remained. Omitting the outlier has been discussed in chapter 4and the missing data in input variables are due to operation shutdown.Recall the discussion in RVP model, we have defined two different reference models in orderto assess the value of prediction error. These are defined as average-model and zero-model. Table 5.10 shows the values of these two reference models along with RMSSEV in bothcalibration and validation. The model is thus accepted since the RMSSEV in validation is lessthan the two reference models. Figure 5.28 shows the prediction error in validation. This figure, along with the correspondinghistogram plot in figure 5.29 are used for the assessment of the obtained prediction error.Figure 5.29 shows a histogram plot of prediction error which exhibit a zero mean error.

It is interesting to study the model performance in validation by applying the new predictedRON value for calculation of the next output. As known, this simulation is called as open-loop


124

simulation, in which it shows the predictability of the model during a period of operationwithout having the actual output measurement. Then, we can compare the model-predictedoutput with the existing RON measurement. This is shown in figure 5.30. Notice that we haveno interpolation in validation output. It can be seen that the model is capable of capturing theessential part of the output variation.

0 50 100 150 200-0.3

-0.2

-0.1

0

0.1

0.2

0.3Error in Validation

Figure 5.28: RON model, prediction error in validation.

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.30

1

2

3

4

5

6

7

8

XBIN

BIN

Error in Validation

Figure 5.29: RON model, histogram plot for prediction error in validation.


125

0 50 100 150 20098

98.5

99

99.5

100

100.5

101

101.5RON, Validation, Open Loop Simulation, OR=3, LV = 4

Sample

RO

N S

imu

late

d(o

) an

d R

ON

LA

B(*

)

Figure 5.30: RON model, Open Loop Simulation in validation.

It is more easier to show the agreement between predicted RON by the model and themeasured RON in figure 5.31.

98 98.5 99 99.5 100 100.5 101 101.5 10298

98.5

99

99.5

100

100.5

101

101.5

102RON, Validation, OR=3, LV = 4

RON Model

RO

N L

AB

Figure 5.31: RON predicted versus RON measured in validation.


126

5.3.4 Benzene Model

The ARX model for prediction of aromatic (benzene) contents of the reformate product incatalytic reformer is presented in the following sections.


The following variables are chosen as the input variables in the benzene model. Selection ofthe variables has been discussed in chapter 4.

1 Mole H2/ Mole C in recycle gas2 % H2 purity in recycle gas 3 Reactor 1 outlet temperature4 Reactor 2 outlet temperature5 Reactor 3 outlet temperature6 Reformate Feed flow rate7 C-401 Reformate flow rate8 C-401 Liquid gas flow rate9 C-401 Reflux flow rate10 C-401 Reboiler temp.11 C-203 Reflux flow rate12 C-203 HVN flow rate13 C-203 LVN flow rate14 C-652 HVBN flow rate15 C-201 Naphtha side stream temperature (Pressure Corrected)16 C-601 Naphtha side stream temperature (Pressure Corrected)17 C-203 Bottom temperature (Pressure Corrected)18 C-652 Bottom temperature (Pressure Corrected)

The total amount of input data is 5627, and 4240 in the calibration and validation data setsrespectively, which correspond to 9 months of operation data in calibration and 6 monthsoperation data in validation. Notice that the data corresponding to the periods of processshutdown and outliers has been omitted. Regarding the output variable, there are only 144 and33 laboratory measurement available in respectively for calibration and validation periods.


The model structure in this case is similar to the structure in the case of RVP model. Based on the discussion in section 5.2 and equation 5.8, effect of y(t-24) for output is taken inthe model along with the inputs. Hence, number of A-parameter na will be one and number ofB-parameters nb are determined along with number of LV by a series of recursive simulationof the model. The criterion in determination of nb and LV is RMSSEV as described earlier inthe case of RVP model.This procedure is performed in the calibration of the model and described in the followingsub-section.


127

5.3.4.3 Calibration

As it is described in the case of both RON and RVP models, a set of suitable delay parameters,optimal model order and number of LV parameter need to be determined. These parametershas been found by numerous recursive simulations. The following delay parameters has been found for the input variables:

K = [2 2 3 3 3 2 1 4 2 1 4 7 7 7 17 17 6 10]

Number of suitable nb and LV are found by a separate series of model simulation examiningnb from 1 to 25 and LV from 1 to an arbitrary value 33. The maximum limit of LV can bechosen according to the discussion in section 5.3.2.3.2 of this chapter.The result is shown in figure 5.32 in which the obtained RMSSEV is shown as a function ofnb and LV. Table 5.11 shows RMSSEV for the first 20 nb. As it can be seen, a local minimumfor the RMSSEV is obtained at nb=2, and LV=10, and another local minimum exist at nb=19,and LV=12. Recall the discussion about approving a model with fewer parameters, the modelwith nb=2, and LV=10 would be a good candidate. Figure 5.33 shows RMSSEV as a functionof LV for nb=2.

ARXOrder

Min.RMSSEV

X-Block Y-Block LV

1 0.2289 93.19 92.32 11

2 0.2287 87.60 92.27 10

3 0.2320 87.34 92.24 10

4 0.2337 88.19 92.25 10

5 0.2341 88.52 92.32 10

6 0.2336 87.36 92.46 10

7 0.2289 86.12 92.58 10

8 0.2286 88.11 92.49 10

9 0.2298 87.99 92.45 10

10 0.2320 90.12 92.76 11

11 0.2308 93.69 93.67 14

12 0.2304 93.42 93.75 14

13 0.2328 93.10 93.85 14

14 0.2320 89.08 92.80 11

15 0.2362 91.16 93.60 13

16 0.2311 89.95 93.06 12

17 0.2244 89.58 93.07 12

18 0.2188 89.21 93.06 12

19 0.2171 88.82 93.16 12

20 0.2219 88.41 93.34 12

Table 5.11 : Minimum RMSSEV for different value of ARX order and LV.


128





Table 5.12 : RMSSE, average-model, and zero-model in validation and calibration

Table 5.12 shows the values of the RMSSE obtained for the average and zero models. Theobtained RMSSEV for nb=2 and LV=10 is compared with the reference models and it can beseen that the obtained model can be acceptable.

0 5 10 15 20 25 30 350

10

20

300.2

0.3

0.4

0.5

0.6Benzene, RMSSEV vs nb and LV

LV

nb

RM

SS

Q

Figure 5.32: RMSSEV as a function of nb and LV.

Hence, we choose LV=10 and nb=2, which means that the number of B-parameters would be36 in this model. Number of A-parameters would be one according the structure of the modeldescribed previously.In order to assess how well the calibration is performed, we begin with examining the plot ofthe prediction error in calibration shown in figure 5.34, which indicate small error.


129

0 5 10 15 20 25 30 350.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38Benzene,RMSSEV for as a function LV for nb = 2

Number of LV

RM

SS

EV

Figure 5.33: RMSSEV as a function of LV for nb=2.

0 50 100 150-0.4

-0.3

-0.2

-0.1

0

0.1

0.2


Figure 5.34: Prediction error in calibration.

Figure 5.35 shows the histogram plot of prediction error in calibration indicating that theresiduals can be considered approximately normal distributed with an approximate zero meanerror.


130

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.30

1

2

3

4

5

6

7

8

XBIN

BIN


Figure 5.35: Histogram plot of prediction error in calibration.

The obtain model is simulated using the calibration data set in which the model predictedoutput is used in the ARX model, so called open-loop simulation, which is shown in figure5.36. It can be seen that the open loop simulation is satisfactory.

0 50 100 1502.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4Benzene, Calibration, Open Loop Simulation

Sample

Ben

zene

Sim

ulat

ed(o

) and

Ben

zene

LA

B(*

)

Figure 5.36: Open- loop model simulation in calibration.


131

0 50 100 1502.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4Benzene, Calibration, OR=2, LV = 10

Sample

Ben

zene

LA

B(*

) and

Ben

zene

Mod

el(o

)

Figure 5.37: Prediction ability in calibration.

Figure 5.37 shows the result for simulation of the model in which the actual outputmeasurement is used for prediction of the next output. It is expected that the developed modelis capable to reproduce the calibration satisfactory. As it can be seen from figure 5.36 and5.37, the model has captured the essential variation in the calibration.

2 2.5 3 3.5 4 4.5 52

2.5

3

3.5

4

4.5

5Benzene, Calibration, OR=2, LV = 10

Benzene Model

Ben

zene

LA

B

Figure 5.38: Benzene contents predicted versus measured in calibration.


132

The result in figure 5.37. can be better seen in figure 5.38, which shows a plot of measuredoutput versus model predicted output.

5.3.4.4 Validation

The validation is performed applying a completely distinct set of data. The input data invalidation set consists of 4240 input-output covering 6 months operation. In this case, afteromitting the outliers and missing data, only 33 laboratory measurements of output remaines. The obtained RMSSEV is 0.229 which shown in table 5.12 along with the values of the tworeference models in both calibration and validation. The model is thus accepted since theRMSSEV is less than the two reference models.

0 5 10 15 20 25 30 35-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3


Figure 5.39: Prediction error in validation.

-0.6 -0.4 -0.2 0 0.2 0.40

0.5

1

1.5

2

2.5

3

XBIN

BIN

Error in Validation

Figure 5.40: Histogram plot of prediction error in validation


133

Figure 5.39 shows the prediction error in validation. It can be seen that there is one point thatproduce a large error. The histogram plot of prediction error is shown in figure 5.40. Noticethat there are extremely few output measurements available in this case.

The plot for the open-loop simulation of the model is shown in figure 5.41. As known, theopen-loop simulation shows the predictability of the model during a period of operationwithout having the actual output measurement. As it can be seen, the prediction by open-loop simulation produce a bias in the middle range ofvalidation set. However, examining the simulation of the model, when the actualmeasurements are used, which can be seen in figure 5.42 and 5.43, indicate that model can beacceptable.

0 5 10 15 20 25 30 352.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4Benzene, Validation, Open Loop Simulation

Sample

Ben

zene

Sim

ulat

ed(o

) and

Ben

zene

LA

B(*

)

Figure 5.41: Open- loop model simulation in validation.

One possible explanation for the poor performance of the model in open-loop simulation isthat there are only 144 output measurements available for calibration of the model for a periodof 9 months. Number of existing measurement for the period of nine months is expected to bearound 270 if the output is measured only once a day.The other explanation could be that the choice of nb and LV is not perfectly suitable. Figure5.32 and table 5.11 show another local minimum for RMSSEV at nb=19 and LV=12. Thischoice would not be appropriate since the total model parameters would become 240 which ismore than the total input-output of 114. Hence, the option of nb=19 and LV=12 is rejecteddue to the risk for overfitting. Better result in for this modeling can be investigated only whenmore data is available. Figure 5.42 shows the result of the simulation when the actual measurements are used inprediction of the next output. Figure 5.43 shows the predicted versus the measured benzenecontents in the validation.


134

From figure 5.42 and 5.43 can be seen that the developed model has captured the essentialvariation in the data. However, more data is needed in order to improve the predictability ofthe model.

0 5 10 15 20 25 30 352.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4Benzene, Validation, OR=2, LV = 10

Sample

Ben

zene

LA

B(*

) and

Ben

zene

Mod

el(o

)

Figure 5.42: Prediction ability in validation.

2 2.5 3 3.5 4 4.5 52

2.5

3

3.5

4

4.5

5Benzene, Validation, OR=2, LV = 10

Benzene Model

Ben

zene

LA

B

Figure 5.43: Benzene contents predicted versus measured in validation.


135

5.4 Conclusion

In this chapter the structure, calibration, and validation of the multivariate predictive modelsdeveloped for quality prediction of reformate product from catalytic reformer I are presented.The corresponding models for prediction of the qualities of reformate and isomerate productsof catalytic reformer II and isomerization unit can be found in appendix A and B respectively.The multivariate models are developed for prediction of RON, RVP, and benzene contents ofthe products.

It is observed that the quality variables are dependent on the earlier values of them selves andthe inputs. This means that an input-output type dynamic modeling approach is a suitablechoice. ARX model is chosen as the model type used in model calibration, in which theparameters are estimated by a PLS model. Applying PLS approach in parameter estimation ofARX model has been useful in which the ability of prediction has increased.

A solution to the problem of low sampling frequency for model output is proposed as follows.

In the case of RVP, and benzene models, a suitable structure of the ARX model is developedin which the information of the pervious available outputs is imposed in the regression vectorof the ARX model. In RVP and benzene models, the data set are informative enough forprediction of these qualities since they are not the target of feed-back control.

The case of applying a full model, i.e. nb=24, for the ARX model has been investigated inRVP modeling, since it is expected that the nb=24 will cover all the variation of the input, andconsequently will result in improving model performance. It is shown that the number of nbcan be reduced without significant loss of predictability by applying a set of optimal delayparameters K and latent variables LV. However, the model with nb=24 is the basic model, andthe reduced model is a special case of the basic model, which only enable modeling of lowfrequency variation in inputs. This conclusion will be thus valid also for other modelsdeveloped later in this work.

In the case of RON, a linear interpolation in output is performed to recover the output incalibration data set, while output interpolation is avoided in validation. It has been found thatthe input-output data set is little informative with respect to the prediction of the output RONdue to the effect of closed-loop control and the effect of little variability of the RON set point.

Consequently, better results are obtained for prediction of RVP and benzene contents of theproducts.

Validation of the benzene model for catalytic reformer I show a poor performance in thesimulation in which the predicted output is used in the model for calculation of the next output(open-loop simulation) while the normal simulation using measured output indicatesatisfactory performance. One explanation for the poor performance of the model in open-loopsimulation is that there are few output measurements available. There are only 144 outputmeasurements available during a period of 9 months for model calibration, while number ofexisting measurements is expected to be around 270 if the output is measured only once a day.Better results in prediction modeling can be investigated only when more qualitymeasurements are available.


136

Chapter 6

Optimization

6.1 Introduction

In this chapter a multi-period optimization model for optimization of gasoline blending ispresented. The optimization model assumes that the prediction models for the streams sent togasoline blending are available. These models are discussed in chapter 5. The objective is tominimize the cost of operation for gasoline production such that the quality and quantitydemands are satisfied. The objective function is a cost function which represent the cost ofoperation for production of blending components plus the inventory cost. This objectivefunction is minimized subject to a set of constraints which represent the demands for qualityand quantity of final gasoline products. The optimum solution will yield in quality and quantityneeded for blend components and with that the optimum value for decision variables. Theseare also called Targets, which will be sent to the advanced control level for implementation. The optimization model assumes that the qualities of final gasoline product is a linear functionof the qualities of the streams sent to the blending unit.A case study is considered as a scenario in production scheduling and the optimum solutionfor this case is discussed.

Chapter 6 Optimization

137

HVN

Reformate

Naphtha Stabilizer/

SplitterSec. 600

Catalytic Reformer ISec. 400

TK-09

MTBETK-1320

TK-30/31

TK-40

TK-35

TK-22LVBN

TK-04D 92

TK-34D 95

TK-33D 98

GasolineBlending

C4TK-28/29

ImportBlendstock

TK-06

HVBN

TK-05D 98

TK-1382TK-1383TK-1375

Export

Isomerization UnitSec. 4600

Isomerate

Deisopentanizer

LVN

LVN


IC5

HVN Reformate

NaphthaStabilizer/Splitter Sec 200

NaphthaStabilizer/

SplitterSec 4700

TK-81

TK-42

TK-23

LVN

Split 2

Split 1

Split 3

Mix 1

Figure 6.1: A schematic diagram of the gasoline blending unit and inventory tanks.


138

6.2 Optimization Model

In this section the optimization model is presented. The model integrates the gasoline blendingand short term production planning for the gasoline blending. Short term implies that thescheduling horizon will be approximately 7-10 days.

6.2.1 Nomenclature

6.2.1.1 Index Sets

The plant consists of a set of objects. These objects are defined by the flow diagram shown infigure 6.1 . Abstractly, these objects are described by the sets:

where I is the set of inventory tanks in the plant.i ∈ I where J is the set of outlet streams of inventory tanks.j ∈ J where N is the set of inlet streams to inventory tanks.n ∈ Nwhere O is the set of all other streams including input and output streams ofo ∈ O

mixing point and splitting points. where K is the set of quality characteristics considered.k ∈ K

where L is the set of gasoline products produced.l ∈ L where M is the set of mixing points in the plant.m ∈ M

where S is the set of splitting points in the plant.s ∈ S where T is the set of time points considered.t ∈ T where U is the set of catalytic reformers, and isomerization units in the plant..u ∈ U

The structure of the plant is defined by the connection of the objects defined by the above sets.The interconnections are defined by the following subsets:

II(i) is the set of inlet streams to tank i , and . i ∈ I II(i) ∈ NOI(i) is the set of outlet streams from tank i, and . i ∈ I OI(i) ∈ JIM(m) is the set of inlet streams to mixing point m, and . m ∈ M IM(m) ∈ OOM(m) is the outlet streams from mixing point m, and . m ∈ M OM(m) ∈ OIS(s) is the inlet streams to split point s, and . s ∈ S IS(s) ∈ OOS(s) is the set of outlet streams to split point s, and . s ∈ S OS(s) ∈ OIU(u) is the set of inlet streams to production unit u, and . u ∈ U IU(u) ∈ OOU(u) is the set of outlet streams from production unit u, and .u ∈ U OU(u) ∈ O

6.2.1.2 Variables

The variables in the model are:

Fjt flow rate (m3/hr) in stream j at time point t.fjt volume (m3) in stream j during the period starting at time point t.Gjt flow rate (m3/hr) in stream N at time point t.gjt volume (m3) in stream n during the period starting at time point t.


139

Hot flow rate (m3/hr) in stream O at time point t.Vit volume (m3) in tank i at time point t.Qikt measure of quality k in tank i at time point t.qjkt measure of quality k in stream j during the period starting at time point t.pnkt measure of quality k in stream n during the period starting at time point t.rokt measure of quality k in stream o during the period starting at time point tWlkt measure of quality k in product l at time point t.VC is the variable cost of products over a given time horizon.

6.2.1.3 Parameters

The parameters in the model are:

Dlt is the demand (m3) for product l in the period starting at time point t.cit is the cost ($/m3), i.e. market price, of the content in tank i in the period starting at time point t.bit is the price ($/m3) of blend stock storage in tank i form time point t to time point t+1. Basically this parameter should be a discount factor accounting for the workingcapital tied up in inventory.

6.2.2 Tank Models

The models for tanks are based on total volume balance and quality characteristic balances, inwhich the qualities are assumed to blend linearly. The dynamic equations in the optimizationmodel are discretized using Euler discretization. Furthermore, the tanks are assumed to be well stirred such that the quality of the effluentstream from the tank is equal to the quality inside the tank. An upper and a lower bound foreach variable is also included in the model.The assumptions mentioned above is listed and summarized as follows:

1 Quality characteristics blend linearly.2 The tanks are well mixed.3 The quality characteristics of an effluent stream from a tank is equal to the quality

characteristics of the material in the tank.4 Each tank has an upper and a lower volume capacity limit.

6.2.2.1 Balance Equations

The total volume balance around tank i is:

dVi(t)dt

= Gn(t) − Fj(t) ∈ II(i), j ∈ OI(i) (6.1)

in which it is assumed that there is only one input, and one output stream for each tank. Thecorresponding Euler approximation can be written as:

dVi(t)dt

≈ Vi(t + ∆t) − Vi(t)∆t = Gn(t) − Fj(t) n ∈ II(i), j ∈ OI(i) (6.2)


140

The discrete time model for the total volume balance of tank i is consequently:

Vi,t+1 = Vit + gnt − f jt n ∈ II(i), j ∈ OI(i) (6.3)Where:

Vit = Vi(t) (6.4)

gnt = ∆t Gn(t) (6.5)

f jt = ∆t Fj(t) (6.6)

Note that Fj(t) is a flow rate (m3 /h ) while fjt is a volume (m3).Similarly, the quality balance equation around each tank:

ddt

(Q ik(t)Vi(t)) = pnk(t)Gn(t) − q jk(t)Fj(t) n ∈ II(i), j ∈ OI(i) (6.7)

is discretized as follows:

Q i,k,t+1Vi,t+1 = Q iktVit + pnktgnt − q jktf jt n ∈ II(i), j ∈ OI(i) (6.8)

where:Q ikt = Q ik(t) (6.9)

q jkt = q jk(t) (6.10)

pnkt = pnk(t) (6.11)

6.2.2.2 Well stirred tank assumption

The assumption of well stirred tank means that the quality of the tank effluent is identical tothe quality of the material in the tank:

q jkt = Q ikt j ∈ OI(i) (6.12)

6.2.3 Mixing Point

The mixing point are modeled by a static total volume balance :

Hαt = Σβ∈IM(m)

Hβt α ∈ OM(m) (6.13)

and static quality balances in which the qualities are assumed to blend linearly:

rαktHαt = Σβ∈IM(m)

rβktHβt α ∈ OM(m) (6.14)


141

6.2.4 Splitting Points

A total volume balance around each split point is :

Hαt = Σβ∈OS(S)

Hβt α ∈ IS(s) (6.15)

The quality of each effluent stream from the splitter is identical to the quality of the inlet to thesplitter stream:

rαkt = rβkt α ∈ IS(s), β ∈ OS(s) (6.16)

6.2.5 Qualities of Isomerate, and Reformate Streams

The qualities of the products from catalytic reformers and isomerization units are calculated bythe chemometric models described in chapter 5. In optimization model they are expressed in ageneral form of function Φ, as follows:

rαkt = Φkt(•) α ∈ OU(u) (6.17)

6.2.6 Blending Model

The qualities of the outlet stream of the gasoline blending unit, which is the final gasolineproduct, are assumed to blend linearly as function of the qualities of the intermediate streamssent to the gasoline blending. It is expressed mathematically as follows:

Wlkt =Σj∈J

q jkt fjt

Σj∈J

fjt

(6.18)

The demand for each product is :

Σj∈J

f jt = D lt (6.19)

Combination of equation 6.12, 6.18, and 6.19 gives :

Wlkt D lt = Σj∈J

Q ikt f jt (6.20)

6.2.7 Restrictions

The quality restrictions for each quality k of each product l is given by upper and lowerbounds:

WlkL ≤ Wlkt ≤ Wlk

U (6.21)

Combination of equation 6.12, 6.18, 6.19, and 6.21 gives :

WlkL D lt ≤ Σ

j∈JQ ikt f jt ≤ Wlk

U D lt (6.22)


142

It is further assumed that there are upper and lower restrictions on the volume of a given blendcomponent used in the final gasoline product.

f jtL ≤

fjt

Σj∈J

fjt

≤ f jtU (6.23)

which can be rearranged to the following equation:

D lt f jtL ≤ f jt ≤ D lt f jt

U (6.24)

6.2.8 Bounds on Variables

A lower and an upper bound on the quality, and material in each tank is added to the model bythe bounds:

ViL ≤ Vit ≤ Vi

U (6.25)

Q iL ≤ Q it ≤ Q i

U (6.26)

WiL ≤ Wit ≤ Wi

U (6.27)

Lower and Upper bounds on the streams is as follows:

G jL ≤ G jt ≤ G j

U j ∈ N (6.28)

H jL ≤ H jt ≤ H j

U j ∈ O (6.29)

To avoid too drastic changes in operation conditions it could be relevant to put limits on thechange of the flows from one period to the next:

∆FjL ≤ Fj,t+1 − Fjt ≤ ∆Fj

U (6.30)

∆GnL ≤ Gn,t+1 − Gnt ≤ ∆Gn

U (6.31)

∆HoL ≤ Ho,t+1 − Hot ≤ ∆Ho

U (6.32)


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6.2.9 Objective Function

It is assumed that the corporate strategy is to run the refinery at full capacity. Therefore theobjective is to produce minimum cost product in such quantities that the demand is satisfied.Consequently the objective function can be stated as follows:

VC = Σt∈T

Σi∈I

Σj∈J

c i f jt + Σt∈T

Σi∈I

b itVit (6.33)

The first term in the objective function accounts for the value of the blend components putinto to the final gasoline products. This term implicitly accounts for the processing cost andprice of raw material used to produce the blend components. In this formulation it is assumedthat the processing cost is independent of the processing conditions and only depends on thethroughput. Independence of production conditions and cost is an assumption which is openfor discussion. In reality there will obviously be some relation between the processingconditions and the costs of the blend components. This relation can be incorporated byconsidering a discrete set of processing and relating the cost coefficients at these discreteprocessing conditions only. If the cost coefficients, i.e. ci are regarded functions of theprocessing conditions the decomposition of the problem presented in the next subsection ofthis chapter will not be possible.The second term accounts for the working capital tied up in carrying an inventory. Basically itrepresent the interest rate paid to finance working capital used for carrying the inventory. It isassumed the coefficients in this term, i.e. bi is constant during the period of optimization, sincethe time horizon of the optimization problem in this formulation is 7-10 days applied for shorttime planning and scheduling.


144

6.2.10 Total Optimization Model

The optimization model is expressed as follows:

min Σ

t∈TΣi∈I

Σj∈J

c i f jt + Σt∈T

Σi∈I

b itVit (6.34)

s.t. Σj∈J

f jt = D lt (6.35)

Wlkt D lt − Σj∈J

Q ikt f jt = 0 (6.36)

Vi,t+1 − Vit − gnt + f jt = 0 n ∈ II(i), j ∈ OI(i) (6.37)

Q i,k,t+1Vi,t+1 − Q iktVit − pnktgnt + Q iktf jt = 0 n ∈ II(i), j ∈ OI(i) (6.38)

Hαt − Σβ∈IM(m)

Hβt = 0 α ∈ OM(m) (6.39)

rαktHαt − Σβ∈IM(m)

rβktHβt = 0 α ∈ OM(m) (6.40)

Hαt − Σβ∈OS(S)

Hβt = 0 α ∈ IS(s) (6.41)

rαkt − rβkt = 0 α ∈ IS(s), β ∈ OS(s) (6.42)

rαkt = Φkt(•) α ∈ OU(u) (6.43)

WlkL D lt ≤ Σ


U D lt (6.44)


U (6.45)

ViL ≤ Vit ≤ Vi

U (6.46)


U (6.47)

WiL ≤ Wit ≤ Wi

U (6.48)

p iL ≤ p it ≤ p i

U (6.49)

G jL ≤ G jt ≤ G j

U j ∈ N (6.50)

H jL ≤ H jt ≤ H j

U j ∈ O (6.51)

∆f jL ≤ f j,t+1 − f jt ≤ ∆f j

U (6.52)

∆GnL ≤ Gn,t+1 − Gnt ≤ ∆Gn

U (6.53)


145

∆HoL ≤ Ho,t+1 − Hot ≤ ∆Ho

U (6.54)

This problem is a nonlinear dynamic optimization problem. The multiperiod gasoline blendingproblem includes gasoline blending unit, the blend component tanks, flow rate and qualities ofthe streams to the blending tanks. The optimal solution to this problem specifies the flow rateand qualities of streams sent to the final gasoline product tank during each time period, thequalities of blend components inside each tank, the qualities of the intermediate products sentto blend component tanks. The optimum solution for the qualities and flow rate of the streams sent to each blendcomponent tank will be the targets for the advanced control level.

Another possibility to facilitate the mathematical tractability of the optimization problemwould be to relax the NLP by linearization of the quality balances. The linearization is basedupon the new variables as presented in the following equations:

v ikt = Q iktVit (6.55)

ynkt = pnkt gnt (6.56)

x ikt = Q iktf it (6.57)

zβkt = rβkt Hβt (6.58)

which are to be used in equations 6.36, 6.38, 6.40, 6.41, and 6.44.


146

6.3 Decomposition

The assumption that the blend component cost is independent of the processing conditionsimplies that the optimization model can be decomposed into sub-problems. One sub-problemis a gasoline blending problem and the other sub-problem is a production planning problem.The gasoline blending problem includes gasoline blending unit including the component andfinal product tanks, and the objective is to produce final products assuming that the qualityand the amount of the blend components are known. The quality variables of the blendcomponents are calculated by using the developed process chemometrics models in this work.The optimal solution to this problem specifies the volume of each component used for the finalproduct, and the qualities of the final gasoline product during each time period.The production planning problem includes calculation of the qualities and volume in tanks, thequalities and flow rate of the streams in the remaining part of the plant. For productionplanning it is assumed that the optimal amount of consumed volume of the blend componenttanks is known and provided by the gasoline blending optimization. Hence, the productionplanning problem solves the quality and material balances in the plant to obtain the targets forthe advanced control level. The basis for this decomposition is that the inlet flows to the component tanks are continuosstream of the products from splitters, catalytic reformers, and isomerization units. However,the contents of component tanks are used only when the gasoline blending is running, andhence the outlet flow of the blend tanks are zero between the batches of the blending.

In summary the production planning problem solves the material balances of the plant andprovides the optimal inlet flow, volume and qualities of the blend component tanks. Thegasoline blending optimization determine the optimal volume of the different blend componentused for production of the desired final product. The decomposition presented here gives a global optimal solution provided that the optimalsolution to the gasoline blending problem makes the production planning problem feasible

6.3.1 Gasoline Blending

The gasoline blending part of the problem covers the plant form the blend component tanks tothe final products, i.e. the downstream section of the gasoline plant. In this formulation it isassumed that volume and the quality variables of the component tanks are known. Thequalities are calculated by the chemometrics models during the last period of filling up thetanks. The flow rate of the streams to the component tanks are measured and hence thevolumes are easily calculated.

minΣ

t∈TΣi∈I

Σj∈J

c i f jt + Σt∈T

Σi∈I

b itVit (6.59)

s.t. Σj∈J

f jt = D lt (6.60)

Vi,t+1 − Vit − gnt + f jt = 0 n ∈ II(i), j ∈ OI(i) (6.61)

WlkL D lt ≤ Σ


U D lt (6.62)


147

Q i,k,t+1Vi,t+1 − Q iktVit − pnktgnt + Q iktf jt = 0 n ∈ II(i), j ∈ OI(i) (6.63)


U (6.64)

ViL ≤ Vit ≤ Vi

U (6.65)


U (6.66)

WiL ≤ Wit ≤ Wi

U (6.67)

iL ≤ p it ≤ p i

U (6.68)

g jL ≤ g jt ≤ g j

U j ∈ N (6.69)

∆f jL ≤ f j,t+1 − f jt ≤ ∆f j

U (6.70)

Consequently, the gasoline blending problem is a dynamic optimization problem, sinceequation 6.61, and 6.63 account for the dynamic term in this formulation. It is further assumedthat the corporate strategy is to run the refinery at full capacity, and hence an estimate of theinlet streams Git will be provided at each time period.

6.3.2 Intermediate Production Planning

The production planning problem consists of the remaining equations i.e. the tanks which arenot used in gasoline blending, isomerization unit, catalytic reformers, splitters, mixing andsplitting points.This problem is considerably smaller than the original problem. And should be solvable at leastlocally.Another and perhaps more realistic model for the production planning would be to includecost of different operation points in the catalytic reformers and isomerization unit as well asthe splitters. This seems necessary as the main objective of the model is to prevent thegive-away which means the quality of the products are better than the desired specificationsfor that product.

6.3.3 Discussion

The weakness of the model formulation above is that, it is assumed that the prices of the blendcomponents are independent of the processing conditions. We should have the prices forreformate and isomerate as a function of octane characteristic or perhaps other qualities.Logically there should be higher prices for higher qualities. This is not the case with thecurrent model. It is not easy to define and determine the relationship between price andquality. However, this restriction can be partly removed by partitioning the characteristics incertain discrete intervals and introducing binary variables indicating which cost region applies.In practice we define different type of products based on certain qualities and determine theprices based on their qualities.


148

6.4 Scheduling

In order to test the optimization model for gasoline blending, a case study is considereddescribed in the following. The name of the production units, products, and tanks refers to thedescription of the process in chapter 2. The flow diagram is shown in figure 6.1. The assumptions are described in the next subsection and a schedule for gasoline production isconsidered by the scenario described in the following. It should be emphasized that theinformation of tank capacity, flow rate, and qualities are fictitious and they just serve as anexample for testing the model.

6.4.1 Assumptions

6.4.1.1 Term

In this test a period of 9 days, i.e. 216 hours, will be considered, which starts from day numberone at 00:00 o'clock and end with day number 10 at 00:00 o'clock.The discretization time interval is 4 hours. This means we get the optimum values every 4hours.

6.4.1.2 Tank Capacity

Let's just assume that we are working with the following capacities. Table 6.1 and 6.2 showthe maximum capacity of the blending component tanks and final gasoline product tanksrespectively.

Blend Component Tank no. Volume ( m3)

MTBE TK-20 1400

Butane TK-28+29 800

Import Naphtha TK-06 16000

LVN TK-09 5000

IC5 TK-30+31 1600

Isomerate TK-23 5000

Isomerate TK-42 5500

Reformate II TK-81 15000

Reformate I+II TK-40 6500

Reformate I TK-35 5000

LVBN TK-22 1500

Total 63300

Table 6.1 : Capacity of Gasoline Blending Component Tanks

It is assumed that a volume of about 5% of maximum tank capacity is the minimum limit forthe inventory tanks. However, the butane gas tanks; i.e. TK 28 and 29, are exception.


149

This will give 60135 m3 maximum volume of all blending components which can be used forblending. It is also assumed that there are orders for seven different type of products assuggested in table 6.2, and the total capacity of this final product tanks is 76200 m3 .

Tank no. Volume (m3) Final Gasoline Products

TK-04 2600 D92

TK-34 7500 D95

TK-05 2600 D98

TK-82 15000 S95

TK-33 7500 S98

TK-83 15000 G91

TK-75 26000 G95

Total 76200

Table 6.2 : Capacity of Final Gasoline Product Tanks

6.4.1.3 Gasoline Blending Input and Output Flow Rate

It is further assumed that the output flow rate of gasoline blending system is 600 m3/hr. Table6.3 shows the assumed upper and lower limits for feed flow rate of different components tothe blending component tanks.

Flow Rate m3/hr

Blend Component Minimum Maximum

LVN 30 100

IC5 4 10

Isomerate 40 70

Reformate 4400 60 85

Reformate 400 30 50

LVBN 4 10

Total 168 325

Table 6.3 : Upper and lower limit for feed to blend component tanks


150

6.4.1.4 Price Index

The component prices used in calculation of the objective function is shown in table 6.4. Theseprices are taken from different issue of Oil & Gas Journal.

Blend Component $/ m3

MTBE 255.10

Butane 108.5

Import Naphtha 168.1

LVN 143.4

IC5 171.4

Isomerate 114.3

Isomerate 114.3

Reformate II 140.2

Reformate I+II 140.2

Reformate I 133.9

LVBN 153.5

Table 6.4: Blend component prices

6.4.2 Gasoline Blending Production Plan

It is further assumed that the blend component tanks are about 50% full at the beginning of theblending period in this scenario. It is thus assumed to be 30000 m3 total volume of all blendingcomponents available at the start of blending period. A minimum total feed flow rate of 168m3/hr to the blending tanks will give 36288 m3 for the whole period of 216 hours. Hence, thetotal volume of all blend stock at the end of the time period would be 66288 m3. Consequently, taking the capacity of the final product tanks under the consideration, it wouldbe possible to plan for a total volume of 64800 m3 of seven final products as suggested in table6.5. The quality specification of the seven products is assumed to be like the suggested valuesin table 6.6. A production plan for the gasoline blending is suggested as shown in table 6.7.

Final Gasoline Product m3/hr Tank no.

D92 4800 TK-04

D95 15000 TK-34

D98 9600 TK-05

S95 10800 TK-82

S98 6000 TK-33

G91 10800 TK-83

G95 7800 TK-75

Total 64800

Table 6.5 : Assumed capacity of final product tanks


151

RON min. RVPkPa

BENZENE max.vol-%

MTBEmax.

vol-%

D92 92 60-95 2.00 10.00

D95 95

D98 98

S95 95 65-95 3.00 11.00

S98 98 65-95

G91 91 60-90 5.00 15.00

G95 95

Table 6.6 : Assumed quality specifications for final products

OrderNo.

Product Date Time Start Time Stop ProductTank No.

Volume(m3)

1 D92 Day 1 00:00 04:00 4 2400

2 D95 Day 1 08:00 16:00 34 4800

3 D98 Day 2 04:00 08:00 5 2400

4 S95 Day 3 00:00 09:00 82 5400

5 S98 Day 3 16:00 21:00 33 3000

6 G91 Day 4 00:00 09:00 83 5400

7 D92 Day 4 20:00 24:00 4 2400

8 G95 Day 5 00:00 05:00 75 3000

9 D98 Day 5 16:00 20:00 5 2400

10 D95 Day 6 08:00 16:00 34 4800

11 G91 Day 7 00:00 09:00 83 5400

12 S98 Day 7 16:00 21:00 33 3000

13 S95 Day 8 00:00 09:00 82 5400

14 D98 Day 8 19:00 23:00 5 2400

15 D95 Day 9 00:00 09:00 34 5400

16 D98 Day 9 16:00 20:00 5 2400

17 G95 Day 10 15:00 23:00 75 4800

TOTAL 64800

Table 6.7 : Orders and production plan


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6.4.3 Results

The value of the objective function is M$ 8.4 for production of 64800 m3 different gasolineproducts. This will give an average cost of $ 0.13 per litter produced gasoline. The multipleblending results for the 17 orders are presented in tables in appendix C. An example of theresult is presented in table 6.8 which shows the results of gasoline blending for order number9. The first two rows in the table is the volume and the qualities of the final product D98. Theseare in good agreement with the demands. The rest of the table 6.8 shows the blendingcomponents volume used in the blend and their actual qualities. Notice that for MTBE,Butane, Import Naphtha, and IC5, the qualities are almost constant. Furthermore, the qualitiesof LVN, LVBN, reformates and isomerate are calculated value, based on the tank model.

Final Product Volumem3

RON Benzenevol%

RVPkpa

D98 2400 98 2 95

Component TimePeriod

Volumem3

MTBE 28 0 0 0 0

Butane 28 290,65 93 0 460

Import 28 0 0 0 0

LVN 28 0 0 0 0

IC5 28 0 0 0 0

Isomerate (42) 28 332,63 89 1 70

Isomerate (23) 28 0 0 0 0

Reformate II 28 893,47 101 5 35

Reformate I+II 28 0 0 0 0

Reformate I 28 883,25 100 0 45

LVBN 28 0 0 0 0

Table 6.8 :Qualities and the volume of the final product and the blend components

The results presented in appendix C exhibit generally good agreement with the demands, andis an indication for a feasible and local optimum solution.


153

6.5 Discussion

An optimization model for operation of the gasoline processing area of the refinery has beendeveloped. The model concerns production of the blend components and gasoline blendingover multiple periods. The model consist basically of material balances, quality requirements,and upper and lower bounds on the variables.The model is decomposed into two sub-problems, one covering the production of the blendcomponents and the other covering the final gasoline product.

The main assumption is that the gasoline qualities blend linearly. This assumption is based onthe results obtained in this work in chapter 3 in which a neural network model is developed forprediction of the qualities of the final gasoline products. The result for this modeling indicatesthat linear approaches can be applied with a reasonable accuracy. Furthermore it is assumedthat the reliable models for prediction of the qualities of isomerate and reformate products areavailable. It is further assumed that the processing cost is independent of the processingconditions and only depends on the throughput.

Although the data used in this scenario is fictitious, but the general evaluation of the multipleblending model is that the solution is a feasible, local optimum solution, and there is goodagreement with the specifications and demands of the products. The value of the objectivefunction in this scenario is M$ 8.4 for production of 64800 m3 different gasoline productswhich gives an average value for the variable cost of $ 0.13 per litter produced gasoline, inwhich a comparison with 1992 prices (Gary, 1994) shows 15% revenue per litter gasoline.Furthermore, the obtained optimum values of the flow rate and qualities of the reformate andisomerate products at the end of the blending period are used as the suggesting target foroperation of these production units.

The main weakness of the model is that the prices of the blend components are independent ofthe processing conditions. Further development of the optimization model should includedetermination of the price of the blend components as a function of qualities. This is also achallenging job, which make the model more complex.


154

Chapter 7

Conclusions

7.1 Introduction

The process of gasoline blending is based on in-line blending of blendstocks, i.e. whilecontinuous feed to the component blend tanks are introduced. In this situation applying thebias-updated regression model for on-line prediction of blend component qualities would notbe adequate since the qualities of the blend stocks will change due to the upstream processvariation. The existing LP plus bias-updating formulation may not handle such time-varyingfeedstock qualities in order to find the optimal solution for the blending problem. Thus,improved and reliable prediction of the qualities in the blendstock tanks are needed based onthe variation of the upstream process as an important basis for optimization of the gasolineblending process.The main purpose of this work has been to develop data-based dynamic models in order topredict the qualities of the blend components and supply the optimization system with theprevious, present and predicted future values of the qualities. The developed models are thenused in a multiperiod nonlinear optimization problem for the gasoline blending.The models are mainly developed for prediction of Research Octane Number (RON), ReidVapor Pressure (RVP), concentration of aromatic compounds, e.g. benzene, in theblendstocks.

Chapter 7 Conclusion

155

The optimization is concentrated around the gasoline blending unit of the refinery, and theobjective is to determine the targets for the advanced control and conventional process controlsystem by minimizing a cost function subject to a set of process and quality constraints in sucha way that the needed quantities of the different final gasoline products can be producedon-time, with the desired specifications. The objective function represent the cost of operationfor production of blending components plus the inventory cost. The objective function isminimized subject to a set of constraints which represent the demands for quality and quantityof final gasoline products, provided the prediction of the qualities of the blend components areavailable.

In the following the conclusions for the modeling and optimization of the gasoline blendingprocess is presented.

7.2 Modeling

7.2.1 Conclusion

Artificial Neural Networks (ANNs) models are developed for prediction of qualities of finalgasoline products using the data from intermediate gasoline blend component tanks. Thesemodels are developed in order to explore nonlinear effects in the blending process. The results for the nonlinear approach for prediction of the qualities for the final gasolineproducts indicate that linear approaches can be applied with a reasonable accuracy. ANNs models exhibit good performance of prediction ability in the case of static nonlinearmodeling. However, when the system exhibit dynamic behavior, static ANN models will notwork. The solution to be investigated in this work is to use a dynamic or time series models.

Principal Component Analysis (PCA) is performed in order to assess the representability of thedata, discover any collinearity in the selected inputs, detection of distinct clusters of data dueto plant operation. The results from PCA analysis have shown that there are systematic variations in data, andhence existence of different operation points in catalytic reformer and isomerization units. Theinteresting observation is that the systematic variations are related mainly to the desired qualityof RON and benzene contents rather than RVP. The RVP specification for final gasolineproduct is different for summer and winter period, but there is no season change forspecification of neither RON nor for benzene content. Consequently, for prediction of RONand benzene contents of the isomerate and reformate products it is not necessary to separatethe modeling into two regions of summer and winter operation. Regarding RVP quality ofisomerate and reformate, there are reasons to believe that one model will be appropriate tocover variation of RVP in both summer and winter period since the operation of reforming andisomerization processes are mainly to maintain the desired RON and benzene content ofreformate and isomerate respectively. A set of suitable input variables is grouped in each modeling case in order to secure a feasiblemodel structure. The main excitation is benzene content which is a set point. Hence thisexcitation signal will be sufficient to ensure identifiability of the benzene loop. Further analysisis necessary for the whole plant section investigated.


156

Multivariate predictive models, applying methods in process chemometrics, are developed forquality prediction of isomerate and reformate products in gasoline processing area. It has been observed that the quality variables are dependent on the previous value ofthemselves and the input variables. This means that a dynamic, time-series modeling approachis a suitable choice in this application. The applied model in this work is ARX (Auto Regressive with Exogenous input) type, inwhich Partial Least Squares Regression (PLS) method is used for parameter estimation.Applying PLS parameter estimation of ARX model has increased the strength of thepredictability by taking advantage of the ability of PLS to extract the useful information fromcollinear, noisy, input data which is relevant for modeling the output prediction.Nonlinear PLS approaches has also been examined in order to explore and model the nonlinearrelationship between input and output. The approaches include Neural Net PLS (NNPLS) andPolynomial PLS. In this work no significant nonlinear relationship has been observed forrelationship between scores in inputs and output.

For the output variables, there are few hourly samples available. The qualities are measuredonly once per day, due to economical consideration and time consuming laboratory analyses.This low sampling frequency for model output has given rise to a challenging problem in thiswork. The solution to this problem is based on the one of the following two situations. If the output variation is slowly moving over one day to the next day, as it is in the case ofRON, a linear interpolation of the output is performed to recover the model output incalibration. However, it is avoided to perform output interpolation in validation. In the opposite case, in which there is a considerable variation in the output signal, indicating apossible faster dynamic response, such as the case of prediction of RVP and benzene contents,it would not be a good solution to replace the missing output by interpolation. The proposedsolution here is that a suitable structure for the ARX model is chosen in which the hourlysampled input variables are used together with the previous existing output measurement,normally measured every 24 hours, in order to model the prediction of output at time t. Thissolution is integrated in the regression matrix of the ARX structure, in which the regressionfor output is over 24 hours whereas the inputs are available every hour.

Another problem is concerned with the cross spectrum between input and the driving noiserealized by output feedback. The control strategy of the reformer and isomerization units isbased on feed-back control of RON quality due to the great importance of octane number onproduction economy. This has effectively caused that the obtained input-output data set isonly little informative with respect to prediction of the output RON due to the effect of anapparently well tuned closed-loop control.

The models are validated using cross validation. Since the model has time-series dynamiccharacteristics, it is important to secure a calibration and validation set containing timesequence of subsequent data. Thus, the validation is performed applying a completely distinctset of data, and it is attempted to cover both winter and summer operation both in thevalidation and calibration data sets. Even if the selected data in calibration cover almost 9-10 months operation and the validationperiod is about 4 months, it must be emphasized that the developed models have a moderategeneral characteristics in which the models are valid only for the operation regions that theyare calibrated for, and hence, implementation of the models for other operations points willneed further calibration. The limited characteristics of the models are due to the effect ofclosed-loop control and low sample frequency of the output. However, under the existing


157

circumstances, the results exhibit acceptable prediction ability and performance of the ARXmodels in time-series regression.

7.2.2 Future Work

By applying the techniques developed in this work attacking the problem of low samplingfrequency, there will be no need for providing a massive amount of quality measurements.Having in mind that a massive amount of quality measurement would not be economicallyfeasible. However, an investment in a reasonable higher sampling rate is recommended for alimited period of time. This can be for instance a sampling rate of two or more laboratoryanalysis per day for a period of few weeks covering both winter and summer operation modes.Regarding elimination of the effect of feedback, a carefully planed experimental design shouldbe performed. There are several methods that can be applied in a closed-loop control in orderto get informative (excited) input-output data set (Nikolaou 1998). An idea in this field can beintroducing an extra input to the regulator which is responsible for adding a controlled extradisturbance to the system.Another direction in predictive quality modeling should be to combine the models for oneproduction unit, and develop Multi Input Multi Output (MIMO) models. This will improve thestrength of the models effectively since there is cross correlation between the inputs and theoutputs used in all models in each production unit.


158

7.3 Optimization

7.3.1 Conclusion

An optimization model for operation of the gasoline processing area of the refinery has beendeveloped. The model concerns production of the blend components mainly in catalyticreformers and isomerization unit, and gasoline blending over multiple periods. It is assumed that the corporate strategy is to run the refinery at full capacity. Therefore theobjective is to produce minimum cost product in such quantities that the demands are satisfied.

The objective function includes the value of the blend components used for the final gasolineproducts, which implicitly accounts for the processing cost and price of raw material used toproduce the blend components. It is thus assumed that the processing cost is independent ofthe processing conditions and only depends on the throughput. A second term in objectivefunction accounts for the working capital tied up in carrying an inventory. It is assumed thatthe interest rate is constant during the period of optimization, since the time horizon of theoptimization problem in this formulation is 7-10 days applied for short time planning andscheduling.

A heuristic decomposition of the model has been performed and two sub-problems areobtained. One covering the production of the blend components and the other coveringgasoline blending.

The multiple period gasoline blending model covers the gasoline blending unit including theblendstocks and final product tanks. It is assumed that the gasoline qualities blend linearly andthe models for prediction of the qualities for isomerate and reformate blendstocks areavailable. The assumption of gasoline linear blending is based on the results of an analysisperformed in this work by a nonlinear approach for prediction of the qualities for the finalgasoline products indicating that linear approaches can be applied with a reasonable accuracy.

The optimization problem is based on available accurate prediction of the qualities in thestreams sent to blendstock tanks reflecting the variation of mainly the reforming andisomerization process.

A case study is considered and production of different types of final gasoline is scheduled in acomplete scenario for a multiple period of blending for a period of 10 days. A feasible localoptimum solution is obtained and the resulting values of optimum variables in this case studyindicate that there is good agreement with the specifications and demands of the final gasolineproducts.A value of the objective function is obtain for this scenario which gives an average value forthe variable cost of $ 0.13 per liter produced gasoline, in which a comparison with 1992 prices(Gary, 1994) shows 15% revenue per liter gasoline.

The obtained optimum values of the flow rate and qualities of the reformate and isomerateproducts at the end of the blending period are used for suggesting an operation target of theseproduction units.


159

7.3.2 Future Work

The multiple period optimization model in this work is developed for the refinery blendingprocess, which is used for the short term planning and scheduling. The future development ofthis model should be in the direction of including a longer time horizon for anintermediate-range planning and scheduling for the gasoline processing area, in which thetargets for flow rate and qualities of the reformate and isomerate products can be determined.This is important for reduction of give-away in which the optimum solution can be found for alarger time horizon and targets can be used for more appropriate planning for the operation ofthe respective units.Further development of the optimization model should also include determination of the priceof the blend components as a function of qualities. This is also a challenging job, which mayadd more nonlinear characteristics to the model, and with that making the model morecomplex.

Real-time application the multiple period gasoline blending optimization model should be oneof the steps in future work, since in-line blending and prediction of the blendstock qualities hasthe potential to provide a competitive benefit for the refinery.


160

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164

Appendix A

Models for CatalyticReformer II

1 Introduction

The developed models for prediction of RON, RVP, and benzene contents of reformateproduct from catalytic reformer II are presented in this appendix. The different steps in modeldevelopment are essentially similar to the procedure applied for the models described inchapter 5.It has been found that the output signal exhibit great correlation to the past values of input andoutput signals. The method used for development of the models is Auto-Regressive withExogenous input (ARX) in which Partial Least Squares Regression (PLS) method is used forits parameter estimation. A description of the plant can be found in chapter 2. The input variables used for the modelsare described in chapter 4, along with a Principal Component Analysis (PCA), and adescription of data treatment. It is expensive to have on-line quality measurements for the reformate product in order to havethe same sampling frequency as the other process variables. The only existing measurement islaboratory analyses which are available only once per day for each quality, i.e. sample rate of24 hours. In the following sections, there will be more focus on model structure, calibration, validation,and performance of the models.

Appendix A

165

2 RVP Model

In this section the model for prediction of Reid Vapor Pressure (RVP) for reformate productfrom catalytic reformer II will be presented.

2.1 Inputs and Output

The following input variables are used in the RVP model.

1 Reactor 1 outlet temperature2 Reactor 2 outlet temperature3 Reactor 3 outlet temperature4 Mole H2/ Mole C in recycle gas5 % H2 purity in recycle gas 6 Reformer Feed flow rate7 C-4401 Feed temperature8 C-4401 Reboiler temperature9 C-4401 Reformate product flow rate10 C-4401 Reflux flow rate11 C-4401 Feed flow rate12 C-4703 Reflux flow rate13 C-4703 LVN flow rate14 C-4703 Reboiler Steam flow rate 15 C-201 Naphtha side stream temperature (Pressure Corrected)16 C-4201 Naphtha side stream temperature (Pressure Corrected)17 C-4703 Bottom temperature (Pressure Corrected)

The output is RVP measured by laboratory, and thus the model will be a Multi Input SingleOutput (MISO) model.The calibration data set is chosen from a period of approximately 9 months operation. Thetotal number of input data in calibration is 7516. The validation data cover approximately 6months operation in which the total number of observation of input data is 2532. As describedin chapter 4, the data corresponding to the periods of process shutdown and outliers has beenomitted. Regarding the output RVP, there are only 305 and 93 laboratory measurementsavailable for calibration and validation periods respectively.

2.2 Model Structure

The model structure is based on an ARX model in which the parameters θ are estimated by aPLS model. The structure of the ARX model is based on a form of regression vector in whichthe hourly sampled input variables are used together with the previous existing output, whichis normally measured at time t-24 hour, in order to model the prediction of output at time t.As described in chapter 5, this solution is integrated in the regression matrix of the ARXstructure, in which the delay time for output is inherently 24 hours. Thus, prediction of thenext output can be calculated using equation A.1, which is derived based on equation 5.8 inchapter 5.

y(t) = a1y(t − 24) + B1U(t − K − 1) + .... + BnbU(t − K − nb) (A.1)

Appendix A

166

in which is the predicted output, U is a vector of input variables, and K is a vector ofy(t)delay parameters for inputs.Hence, there will be only one A-parameter, i.e. na=1, and number of B-parameters nb will beas many as it is necessary to get an acceptable low prediction error, compared to the definedreference models described later.In parameter estimation a PLS model is used. A suitable number of principal components orLatent Variable LV need to be found. Thus, two sets of parameters in model development, i.e.nb and number of LV, has to be determined. This task is handled by developing a recursiveroutine in Matlab, in which the Root Mean Sum Squares Error in Validation (RMSSEV) isused as the criterion for optimum number of nb and LV. RMSSEV is defined as the following.

RMSSEV =Σi=1

n

(y i − y i)2

n (A.2)

where is the model predicted output, yi is the output measurement, which is only RVP iny i

this case, and n is the total number of y. The results for these simulations are described in the next subsection.

2.3 Calibration

As discussed in chapter 5, and expressed in equation A.1, three parameters have to bedetermined. These are optimum number of ARX order i.e. nb, number of LV, and delayparameter for each variable. In this work, the delay parameters are determined by recursive simulations, in which the searchfor delay parameters is limited by some qualified estimate according to process knowledge andphysical restrictions, and then let the model find the best delay parameters found for minimumRMSSEV. The following delay parameters has been found for the input variables in this model:

K = [3 4 4 2 2 1 3 1 1 1 3 11 5 11 1 18 6]

The search for optimum number of ARX order for input variables, i.e. nb, and number of LVis carried out by a series of separate recursive simulations, in which number of nb and LV arechanged from 1 to 25 for nb, and from 1 to 35 for number of latent variables (LV). The choicefor maximum number of LV is based on the following considerations.Number of LV is a function of number of variables, and ARX order, as shown in equationA.3.

Max. LV = na ⋅ ny + nb ⋅ nu (A.3)

where ny is the number of output, and nu is the number inputs variables.In this case na = 1, ny = 1, and nu =17. For nb=2, there will be 35 maximum number for LV. Selecting more LV is disadvantageous, in which it will add more noise to the structure part.Moreover, total number of model parameters will increase by choosing more LV, which is notdesirable, due to the risk of overfitting. These issues are discussed in chapter 3For these reasons, maximum number of 35 LV has been chosen in this case for all nb largerthan 2.

Appendix A

167

Figure A.1 shows the calculated RMSSEV as a function of nb and LV, for nb from 2 to 25and LV from 1 to 35. It can be seen that minimum RMSSEV can be found for LV= 4. In table A.2, the minimumRMSSEV and number of LV at the minimum are shown for nb from 1 to 20. The results fornb larger than 20 are skipped since the value of RMSSEV increase for the rest of the nb. It canbe seen that the minimum RMSSEV is found for nb=2 with LV = 4. Furthermore, there is aregion of nb=15 and nb=16 that RMSSEV has another local minimum, which is not a goodmodel candidate due to the large model parameters. Based on evaluation of the model performance in validation the case with nb=2 and LV=4 ischosen as the best model in this case.

0 5 10 15 20 25 30 350

10

20

302

3

4

5

6

7

8RVPLAB, RMSSEV VS nb and LV

LV

nb

RM

SS

EV

Figure A.1 : RVP Model, RMSSEV as a function of nb and LV.

The obtained RMSSEV for nb=2 is compared with the reference models, i.e. theaverage-model RMSEAVGV and the zero-model RMSEZROV, as it is shown in table A.1.The reference models are described in chapter 3, section 3.6 and has been used in descriptionof the models for catalytic reformer I in chapter 5.





Table A.1 : RVP model, RMSSE, average-model, and zero-model in validation andcalibration.

Appendix A

168

As it can be seen in table A.1 the value of RMSSEV and RMSSEC, which are the obtainedRoot Mean Sum Squares Error in model validation and calibration respectively, are less thanRMSSE for average-model and zero-model both in validation and calibration.

nb Min. RMSSEV X-Block Y-Block LV

1 2.188 76.69 48.31 4

2 2.125 78.01 49.71 4

3 2.137 78.22 49.36 4

4 2.165 78.28 49.37 4

5 2.187 78.03 49.46 4

6 2.211 77.95 49.10 4

7 2.229 77.81 48.77 4

8 2.231 77.56 48.69 4

9 2.241 77.32 48.76 4

10 2.240 77.07 48.62 4

11 2.231 76.85 48.46 4

12 2.225 75.62 48.51 4

13 2.214 75.08 48.52 4

14 2.220 74.99 48.53 4

15 2.217 74.02 48.55 4

16 2.216 74.07 48.47 4

17 2.220 74.04 48.39 4

18 2.229 74.07 48.37 4

19 2.234 74.13 48.18 4

20 2.244 74.19 48.04 4

Table A.2 : RVP model, Minimum RMSSEV for different nb.

The plot for RMSSEV as a function of LV for nb=2 is shown in figure A.2, which showsclearly that the local minimum appears at LV=4.

Appendix A

169

0 5 10 15 20 25 30 352

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6


Number of LV

RM

SS

EV

Figure A.2 : RVP Model, RMSSEV as a function of LV for nb =2.

0 50 100 150 200 250 300 350-15

-10

-5

0

5

10


Figure A.3 : RVP Model, prediction error in calibration.

Following the procedure described in chapter 5, the next step is model calibration. Theprediction error in calibration for this model is shown in figure A.3. Notice that the obtainedRMSSE in calibration is 2.66 kP RVP. Figure A.4 is also used for the assessment ofcalibration. It can be seen that the histogram of error in calibration shown in figure A.4 exhibitan approximate zero mean error.

Appendix A

170

-15 -10 -5 0 5 10 150

5

10

15

20

25

XBIN

BIN


Figure A.4 : RVP Model, histogram plot of prediction error in calibration

Performance of the model in calibration can be evaluated by simulation of the model usingcalibration data. The simulation is performed using the obtained parameters. As described inchapter 5, an open-loop simulation can be used for assessment of model calibration. In thissimulation the model predicted output at time t is used in the model instead of outputmeasurement in order to predict the output value at time t+1. The result for this simulation isshown in figure A.5. The open loop simulation will show the predictability of the model duringa period of operation without having the actual output measurement.

0 50 100 150 200 250 300 35020

25

30

35

40

45


Sample

RV

P S

imul

ated

(o) a

nd R

VP

LA

B(*

)

Figure A.5: RVP Model, Open Loop Simulation in calibration

Appendix A

171

0 50 100 150 200 250 300 35020

25

30

35

40

45

50RVP LAB, Calibration, OR=2, LV = 4

Sample

RV

P L

AB

(*) a

nd R

VP

Mod

el(o

)

Figure A.6: RVP Model, prediction ability in calibration

Figure A.6 shows the result for simulation of the model in which the actual outputmeasurement is used for prediction of the next output. This simulation is performed in order toassess the calibration of the model. It is expected that the developed model is capable toreproduce the calibration satisfactory.As it can be seen from figure A.6 and A.5, the model has captured the essential variation ofRVP. The result in figure A.6 can be better expressed in figure A.7. Figure A.7 showsmeasured RVP at laboratory versus model predicted RVP in calibration. It can be seen thatalthough the model has captured the essential variation but it has difficulty to capture the highfrequency variation of RVP.

Appendix A

172

25 30 35 40 45 5020

25

30

35

40

45

50RVP LAB, Calibration, OR=2, LV = 4

RVP Model

RV

P L

AB

Figure A.7 : Measured RVP vs. model predicted RVP in calibration.

Selection the best nb and LV is based on performance of the obtained model in validation. Theimportant issue is to capture the maximum effect of input variables on prediction of output andobtain a model with minimum prediction error. The issues in validation of the selected modelis discussed in the following subsection.

2.4 Validation

As mentioned earlier in section 2.1, the validation data set is chosen from a period ofapproximately 6 months operation in which the total number of observation of input data is2532. The data corresponding to the periods of process shutdown and outliers has beenomitted, and thereby there are only 93 laboratory measurements of output RVP available forthe validation period.As discussed in the calibration section, a suitable model with fewer model parameters ischosen among a set of model candidate. The selected model has the following parameters. The order of the ARX model is: na = 1, and nb = 2. Number of latent variable in PLSregression LV is equal to 4. The following delay parameters has been found for each inputvariables:

K = [3 4 4 2 2 1 3 1 1 1 3 11 5 11 1 18 6]

The RMSSE in validation, the average-model RMSEAVGV and the zero-model RMSEZROVare shown in table A.1. It can be seen that the RMSSEV is less than average- and zero-model,indicating that the model has captured the essential variation both in input and output.

The prediction error and a histogram plot of error in the validation are shown in figure A.8and A.9. As it can be seen the error is less than in calibration, however a small bias exists.

Appendix A

173

Notice that the error here is the difference between model output and RVP measured at thelaboratory, and the error value is not calculated based on autoscaled data, but it has the realunit, i.e. kPa.

0 20 40 60 80 100-6

-4

-2

0

2

4


Figure A.8: RVP Model, prediction error in validation.

-6 -4 -2 0 2 4 60

1

2

3

4

5

6

XBIN

BIN

Error in Validation

Figure A.9: RVP Model, histogram plot of prediction error in validation.

Another way to evaluate the model performance is an open-loop simulation of the model.Open-loop simulation is performed by letting the new predicted value of the output be usedinstead of measurement for prediction of the next output value. Open-loop simulation will tellus how well the model will predict the output values during a period of operation withouthaving the actual output measurement. It is interesting to see the open-loop simulation of the obtained RVP model using validationdata set, which is shown in figure A.10.

Appendix A

174

0 20 40 60 80 10032

34

36

38

40

42

44

46


Sample

RV

P S

imul

ated

(o) a

nd R

VP

LA

B(*

)

Figure A.10: RVP Model, Open Loop Simulation in validation

As we can see the model has actually captured the essential variation and follow the variationof RVP op and dawn, indicating acceptable performance.

0 20 40 60 80 10032

34

36

38

40

42

44

46

48RVP LAB, Validation, OR=2, LV = 4

Sample

RV

P L

AB

(*) a

nd R

VP

Mod

el(o

)

Figure A.11 : RVP Model, prediction ability in validation

Appendix A

175

30 35 40 45 5030

32

34

36

38

40

42

44

46

48

50RVP LAB, Validation, OR=2, LV = 4

RVP Model

RV

P L

AB

Figure A.12: RVP model predicted versus RVP measured in validation

Figure A.11 shows the result of the simulation when the actual measurements are used. It isobvious from figure A.11 and A.12 that these two simulations are similar. This similarity is anindication that the calibration has captured the essential variation in the input data. FigureA.12 shows RVP predicted versus RVP measured in validation.

Parameter Coef.for(t-1)

Coef. for(t-2)

Sign Description

A 0.1961 0.0000 + Previous RVP

B8 -0.1546 -0.1717 - C-4401 Reboiler temp.

B10 -0.1789 -0.2200 - C-4401 Reflux flow rate

B12 -0.0219 -0.0165 - C-4703 Reflux flow rate

Table A.3 : The largest parameters in RVP model.

Table A.3 shows a list of the parameter values of those variables that have the largest effect onthe RVP. The same discussion as in chapter 5 is valid here for interpretation of the effect ofdifferent input variables.There is only one A-parameter, which is the effect of the last measured RVP. The largesteffects of input variables come from variables number B8 (stabilizer C-4401 reboilertemperature) and B10 (stabilizer C-4401 reflux flow rate) both with negative effects. Thisnegative effects are correct since an increment in both reboiler temperature and reflux flowrate will decrease RVP as a result of removing more light hydrocarbon components from thebottom product (the reformate product).

Appendix A

176

Variable number B12 is the reflux flow rate in the naphtha splitter, in which its main objectiveis to split naphtha into LVN and HVN. Increment in the reflux flow rate of the splitter meansmore light components toward LVN and more heavy component to HVN, and by that anegative effect on RVP.The rest of the variables is considered to have less effect on RVP.

Appendix A

177

3 RON Model

3.1 Introduction

In this section the model for prediction of Research Octane Number RON for reformateproduct from catalytic reformer II will be presented.


It has been found that the following variables have the most effect on output RON.

1 Reactor 1 outlet temperature 2 Reactor 2 outlet temperature3 Reactor 3 outlet temperature4 Mole H2/mole C in recycle gas5 % H2 purity in recycle gas6 Reformer feed flow rate

The total number of input data is 7515, and 2527 in calibration and validation data setrespectively. These number of data set corresponds to 11 months operation data in calibrationand 4 months operation data in validation. Notice that the data corresponding to the periods ofprocess shutdown and outliers has been omitted. Regarding the output RON, there are only331 and 100 laboratory measurements available in the calibration and validation periodsrespectively.

3.3 Model Structure

The RON quality is the main control variable in the catalytic reformer. Effective feedbackcontrol, based on manipulating the temperature of the inlet streams to the reactors, has causedsmall variation in the RON quality, as it is shown in table A.4. Notice that this is thecalibration data set that cover 11 months of operation. It has been found that the type of model structure used in the case of RVP model is notsuitable for prediction of RON. As it is shown in chapter 4, there is more variation in the RVP.This is particularly due to the control strategy in the reformer unit, which is based on effectivecontrol of RON quality.

Calibration Reactor Outlet Temperature

RON R1 R2 R3

Average 101.00 391.80 446.91 472.33

Std. Deviation 0.25 3.28 5.36 4.98

Maximum 101.80 398.77 458.23 482.95

Minimum 100.00 380.81 432.86 459.88

Table A.4 : Calibration data set, RON and reactor outlet temperatures

Appendix A

178

As it is discussed in chapter 5, linear interpolation is performed in order to estimate themissing RON values. This is consequently based on the assumption that the variation of RONfrom one day to another is small enough to permit a rough estimation of RON between twosubsequent existing RON measurement. Since we are applying interpolation in order to estimate the missing RON output, we will havean equal number of observations in both input and output data set. The number ofA-parameters, and B-parameters are then determined by model order, and we will have thesame number of na, and nb. The model structure is based on an ARX model, in which PLS isused for parameter estimation.It is important to emphasize that the interpolation is performed only in calibration data set. Inthe validation, we let the model apply its own predicted output, in order to predict the nextoutput.

3.4 Calibration

As it is described earlier, we need to find a set of suitable delay parameters, optimum numberof model order and LV parameter. These parameters has been found by numerous recursive simulations. The following delayparameters has been found for the input variables:

k = [20 20 19 6 6 5]


Table A.5. shows the values of RMSSV obtained for the different ARX orders and LV, inwhich the model order is changed from 1 to 25 in order to search for all possible effect ofvariables up to t-24, i.e. the previous measured RON. It can be seen that a local minimum appear already by a second order ARX model and LV=3,the value of RMSSEV is 0.045. Furthermore, the value of RMSSEV can not be much lessthan 0.03 for all possible ARX orders and all LVs, and another local minimum appear atnb=10, LV= 6, which gives RMSSEV= 0.032.The progress of RMSSEV for different LV is shown in figures A.13 for the first ARX order,and in figure A.14 for the 10th ARX order. Notice that in these figures only that part of thediagram is shown that include the minimum. The rest of the plot is skipped because includingmore LV produce large RMSSEV.

As discussed in chapter 5, it is preferable to choose a model structure with fewer parameters.Hence, the model structure with nb=2, and LV=3 is chosen, since the difference betweenRMSSEV in this case and the next local minimum is small.

It is important to notice again that these RMSSEV values is calculated based on that themodel apply its own predicted output in order to predict the next output. In other word theseare the values of RMSSEV in open-loop simulation of the model.

Appendix A

179

ARX Order Min. RMSSEV X-Block Y-Block LV

1 0.1950 99.28 98.68 5

2 0.0446 86.72 97.88 3

3 0.0444 86.62 96.97 3

4 0.0476 86.51 95.89 3

5 0.0434 98.76 98.78 7

6 0.0374 98.39 98.60 6

7 0.0318 96.28 98.42 5

8 0.0328 96.12 98.25 5

9 0.0324 97.39 98.14 6

10 0.0316 97.42 97.90 6

11 0.0318 97.27 97.66 6

12 0.0324 97.09 97.43 6

13 0.0335 96.88 97.18 6

14 0.0349 97.94 98.56 9

15 0.0355 97.84 98.49 9

16 0.0360 97.74 98.42 9

17 0.0362 97.63 98.35 9

18 0.0364 97.52 98.27 9

19 0.0371 97.40 98.20 9

20 0.0375 98.43 98.77 13

21 0.0375 98.34 98.76 13

22 0.0369 98.00 98.67 12

23 0.0363 97.90 98.66 12

24 0.0358 97.80 98.65 12

25 0.0354 97.70 98.64 12

Table A.5 : Minimum RMSSEV for different value of ARX order and LV.

Appendix A

180

1 2 3 4 5 60.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1RMSSEV for as a function LV for nb = 1

Number of LV

RM

SS

EV

Figure A.13: RON model, RMSSEV as a function of LV for nb=1.

0 2 4 6 8 10 120.02

0.04

0.06

0.08

0.1

0.12

0.14


Number of LV

RM

SS

EV

Figure A.14: RON model, RMSSEV as a function of LV for nb =10.

The prediction error for this model is shown in figure A.15. Notice that the size of the data setin calibration is 7515 observations. However, number of actual measured RON by laboratoryis only 331. In figure A.15, only the error corresponding to existing measured RON is shown,and the error corresponding to interpolated data is omitted. It can be seen that the predictionerror is small.

Appendix A

181

0 50 100 150 200 250 300 350-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15


Figure A.15: RON model, prediction error in calibration.

0 50 100 150 200 250 300 350100

100.2

100.4

100.6

100.8

101

101.2

101.4

101.6

101.8RON, Calibration, Open Loop Simulation

Sample

RO

N S

imul

ated

(o) a

nd R

ON

LA

B(*

)

Figure A.16: RON model, open loop simulation in calibration.

Figure A.16 shows the open-loop simulation of the model by using calibration data set.Open-loop simulation is performed by letting the new predicted value of the output be usedinstead of measurement for prediction of the next output value. It can be seen that theprediction ability is satisfactory.

Appendix A

182

0 50 100 150 200 250 300 350100

100.2

100.4

100.6

100.8

101

101.2

101.4

101.6

101.8RON, Calibration, OR=2, LV = 3

Sample

RO

N L

AB

(*) a

nd R

ON

Mod

el(o

)

Figure A.17: RON model, prediction in calibration.

99 99.5 100 100.5 101 101.5 10299

99.5

100

100.5

101

101.5

102RON, Calibration, OR=2, LV = 3

RON Model

RO

N L

AB

Figure A.18: Measured RON vs. model predicted RON in calibration.

Figure A.17 shows the result for simulation of the model in which the actual outputmeasurement is used for prediction of the next output. This simulation is performed in order toassess the calibration of the model. It is expected that the developed model is capable toreproduce the calibration satisfactory.

Appendix A

183

As it can be seen from figure A.16 and A.17, the model has captured the essential variation ofRON. The result in figure A.17 can be better expressed in figure A.18, which shows measuredRON at laboratory versus model predicted RON in calibration.

Figure A.19 shows the histogram plot of prediction error in calibration, which exhibits anapproximate zero mean error.

-0.3 -0.2 -0.1 0 0.1 0.20

5

10

15

20

25

30

XBIN

BIN


Figure A.19: RON model, histogram plot for prediction error in calibration.

3.5 Validation

The validation is performed applying a completely distinct set of data. As mentioned beforethe input data in validation set consists of 2527 data set covering 4 months operation. In thisperiod, after omitting the outliers, there are only 100 laboratory measurements of output RONis remained.

The RMSSE in validation, the average-model RMSEAVGV and the zero-model RMSEZROVare shown in table A.6. It can be seen that the RMSSEV is less than average- and zero-model,indicating that the model has captured the essential variation both in input and output.





Table A.6: RMSSE, average-model, and zero-model in validation and calibration.

Appendix A

184

The prediction error in the validation is shown in figure A.20. Notice again that in figure A.20,only the error corresponding to existing 100 measured RON is shown. It can be seen that theprediction error is small.

0 20 40 60 80 100 120-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25


Figure A.20: RON model, prediction error in validation.

0 20 40 60 80 100 120100.4

100.6

100.8

101

101.2

101.4

101.6RON, Validation, Open Loop Simulation

Sample

RO

N S

imul

ated

(o) a

nd R

ON

LA

B(*

)

Figure A.21: RON model, open loop simulation in validation.

Figure A.21 shows the open-loop simulation in the validation, in which the predicted value ofthe output is used to predict the next output value. It can be seen that the prediction ability issatisfactory.

Appendix A

185

The result in figure A.21 can be better expressed in figure A.22, which shows measured RONat laboratory versus model predicted RON in validation. Figure A.23 shows the histogram plot of prediction error in validation, which exhibits anapproximate zero mean error.

99 99.5 100 100.5 101 101.5 10299

99.5

100

100.5

101

101.5

102RON, Validation, OR=2, LV = 3

RON Model

RO

N L

AB

Figure A.22: Measured RON vs. model predicted RON in validation.

-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.30

2

4

6

8

10

12

14

XBIN

BIN

Error in Validation

Figure A.23: RON model, histogram plot for prediction error in validation.

Appendix A

186

4 Benzene Model

In this section the model for prediction of benzene (aromatics) contents of reformate productfrom catalytic reformer II will be presented.


The following input variables are used in the benzene model.

1 Reactor 1 outlet temperature2 Reactor 2 outlet temperature3 Reactor 3 outlet temperature4 Mole H2/ Mole C in recycle gas5 % H2 purity in recycle gas 6 Reformer Feed flow rate7 C-4401 Feed temperature8 C-4401 Reboiler temperature9 C-4401 Reformate product flow rate10 C-4401 Reflux flow rate11 C-4401 Feed flow rate12 C-4703 Reflux flow rate13 C-4703 LVN flow rate14 C-4703 Reboiler Steam flow rate 15 C-201 Naphtha side stream temperature (Pressure Corrected)16 C-4201 Naphtha side stream temperature (Pressure Corrected)17 C-4703 Bottom temperature (Pressure Corrected)

The output is benzene contents (wt%) measured by laboratory. The total number of input dataare 7516, and 2532 in calibration and validation data set respectively. These number of dataset corresponds to 11 months operation data in calibration and 4 months operation data invalidation. Notice that the data corresponding to the periods of process shutdown and outliershas been omitted. Regarding the output benzene, there are only 328 and 103 laboratorymeasurements available in the calibration and validation periods respectively.

4.2 Model Structure

The model structure in benzene model is similar to the structure of the model in RVP case. Itis based on an ARX model in which the parameters are estimated by the PLS regressionmodel. As it is discussed in the RVP model, and shown in equation A.1, the effect of previousoutput y(t-24) is taken along with the hourly sampled input variables. As described in chapter5, this solution is integrated in the regression matrix of the ARX structure, in which the delaytime for output is inherently 24 hours. Hence, there will be only one A-parameter, i.e. na=1, and number of B-parameters nb will beas many as it is necessary to get an acceptable low prediction error. In parameter estimation aPLS model is used. A suitable number of principal components or Latent Variable LV need tobe found. Number of LV, and nb are determined by a series of recursive simulations, in whichthe Root Mean Sum Squares Error in Validation (RMSSEV) is used as the criterion foroptimum number of nb and LV.

Appendix A

187

4.3 Calibration

The following delay parameters has been found for the input variables:

K = [3 4 4 2 2 1 3 1 1 1 3 11 5 11 1 18 6]

Table A.7. shows the values of RMSSEV obtained for the different ARX orders, in which themodel order is changed from 1 to 25 in order to search for all possible effect of variables up totime t-24. Figure A.24 shows a plot of the obtained RMSSEV for nb from 2 to 25, and LVfrom 1 to 35. Figure A.25 shows the RMSSEV for nb=1.


1 0.127 67.21 86.96 2

2 0.132 67.08 86.14 2

3 0.135 66.98 85.69 2

4 0.138 66.86 85.37 2

5 0.139 66.72 85.08 2

6 0.141 66.58 84.79 2

7 0.127 97.70 92.33 13

8 0.109 96.16 91.86 11

9 0.104 95.89 91.96 11

10 0.111 95.69 92.06 11

11 0.134 95.42 92.04 11

12 0.147 65.01 83.10 2

13 0.146 95.22 92.49 12

14 0.139 94.93 92.54 12

15 0.129 94.50 92.60 12

16 0.131 94.10 92.66 12

17 0.145 93.87 92.74 12

18 0.154 64.06 81.55 2

19 0.156 64.03 81.30 2

20 0.157 64.01 81.07 2

21 0.159 63.99 80.85 2

22 0.162 63.98 80.63 2

23 0.164 63.96 80.41 2

24 0.166 63.94 80.20 2

25 0.168 63.92 79.98 2

Table A.7 : Minimum RMSSEV for different value of ARX order and LV.

Appendix A

188

It can be seen that a local minimum appear already by first and second order ARX model andLV=2. Furthermore, another local minimum appear at nb=9, LV= 11, which is also shownseparately in figure A.26.As discussed in chapter 5, it is preferable to choose a model structure with fewer parameters.Hence, the model structure with nb=2, and LV=2 is chosen, since the difference betweenRMSSEV in this case and the next local minimum is small.

0 5 10 15 20 25 30 350

5

10

15

20

25

0.1

0.2

0.3

0.4Benzene, RMSSEV VS nb and LV

LV

nb

RM

SS

EV

Figure A.24: RMSSEV as a function of nb and LV.

0 5 10 15 200.12

0.14

0.16

0.18

0.2

0.22

0.24


Number of LV

RM

SS

EV

Figure A.25: RMSSEV as a function of LV for nb=1.

Appendix A

189

0 5 10 15 20 25 30 350.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26


Number of LV

RM

SS

EV

Figure A.26: RMSSEV as a function of LV for nb=9.

The prediction error for this model is shown in figure A.27. Notice that the actual number of measured benzene contents by laboratory is only 328. In figure A.27 only the errorcorresponding to existing measured output is shown. It can be seen that the prediction error issmall. Figure A.28 shows the histogram plot of prediction error in validation, which exhibitsan approximate zero mean error.Figure A.29 shows the open-loop simulation in the calibration, in which the predicted value ofthe output is used to predict the next output value. It can be seen that the prediction ability issatisfactory.

0 50 100 150 200 250 300 350-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6


Figure A.27: Prediction error in calibration.

Appendix A

190

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80

2

4

6

8

10

12

14

16

XBIN

BIN


Figure A.28: Histogram plot for prediction error in calibration.

Figure A.30 shows the result for simulation of the model in which the actual outputmeasurement is used for prediction of the next output. It is expected that the developed modelis capable to reproduce the calibration satisfactory. As it can be seen from figure A.29 andA.30, the model has captured the essential variation of the output.Figure A.30 shows the result for simulation of the model in which the actual outputmeasurement is used for prediction of the next output. It is expected that the developed modelis capable to reproduce the calibration satisfactory. As it can be seen from figure A.29 andA.30, the model has captured the essential variation of the output.

Figure A.30 shows the result for simulation of the model in which the actual outputmeasurement is used for prediction of the next output. It is expected that the developed modelis capable to reproduce the calibration satisfactory. As it can be seen from figure A.29 andA.30, the model has captured the essential variation of the output.

Appendix A

191

0 50 100 150 200 250 300 3500.5

1

1.5

2

2.5

3Benzene, Calibration, Open Loop Simulation

Sample

Ben

zene

Sim

ulat

ed(o

) and

Ben

zene

LA

B(*

)

Figure A.29: Open loop simulation in calibration.

0 50 100 150 200 250 300 3500.5

1

1.5

2

2.5

3Benzene, Calibration, OR=2, LV=2

Sample

Ben

zene

LA

B(*

) and

Ben

zene

Mod

el(o

)

Figure A.30: Prediction in calibration.

Appendix A

192

The result in figure A.30 can be better expressed in figure A.31, which shows measured versusmodel predicted benzene contents in calibration.

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3Benzene, Calibration, OR=2, LV=2

Benzene Model

Ben

zene

LA

B

Figure A.31: Measured vs. model predicted benzene contents in calibration.

4.4 Validation

The validation is performed applying a completely distinct set of data. As mentioned beforethe input data in validation set consists of 2532 data set covering 4 months operation. In thisperiod, after omitting the outliers, there are only 103 laboratory measurements of output isremained. The RMSSE in validation, the average-model RMSEAVGV and the zero-model RMSEZROVare shown in table A.8. It can be seen that the RMSSEV is less than average- and zero-model,indicating that the model has captured the essential variation both in input and output.





Table A.8: RMSSE, average-model, and zero-model in validation and calibration.

The prediction error in the validation is shown in figure A.32. Notice again that in figure A.32,only the error corresponding to existing 103 measured output is shown. It can be seen that theprediction error is small.

Appendix A

193

0 20 40 60 80 100 120-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6


Figure A.32: Prediction error in validation.

Figure A.33 shows the histogram plot of prediction error in validation, which exhibits anapproximate zero mean error. Figure A.34 shows the open-loop simulation in the validation, in which the predicted value ofthe output is used to predict the next output value. It can be seen that the prediction ability issatisfactory.

-0.4 -0.2 0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7

XBIN

BIN

Error in Validation

Figure A.33: Histogram plot for prediction error in validation.

Figure A.35 shows the result of the simulation when the actual measurements are used. It canbe seen from figure A.34 and A.35 that the calibration has captured the essential variation inthe input. It can also be seen that there are two distinct region in the output values; onearound 1.4% and another around 2.1% benzene. The developed model is capable to coverboth region at the same time.

Appendix A

194

0 20 40 60 80 100 1201

1.5

2

2.5Benzene, Validation, Open Loop Simulation

Sample

Ben

zene

Sim

ulat

ed(o

) and

Ben

zene

LA

B(*

)

Figure A.34: Open loop simulation in validation.

0 20 40 60 80 100 1201

1.5

2

2.5Benzene, Validation, OR=2, LV=2

Sample

Ben

zene

LA

B(*

) and

Ben

zene

Mod

el(o

)

Figure A.35: Prediction in validation.

The result in figure A.35 can be better expressed in figure A.36, which shows measured versusmodel predicted benzene contents in validation.

Appendix A

195

1 1.5 2 2.5 31

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3Benzene, Validation, OR=2, LV=2

Benzene Model

Ben

zene

LA

B

Figure A.36: Measured benzene vs. model predicted benzene in validation.

Appendix A

196

Appendix B

Models for IsomerizationUnit

1 Introduction

The developed models for prediction of RON, and RVP for isomerate product fromisomerization unit are presented in this appendix.

The different steps in model development are essentially similar to the procedure applied forthe models described in chapter 5, and appendix A.

A description of the plant can be found in chapter 2. The input variables used for the modelsare described in chapter 4, along with a Principal Component Analysis (PCA), and adescription of data treatment.

In this appendix, there will be more focus on model structure, calibration, validation, andperformance of the models. The reader is encouraged to see chapter 5 for more detail.

Appendix B

197

2 RVP Model

In this section the model for prediction of Reid Vapor Pressure (RVP) for isomerate productfrom isomerization unit will be presented.


The following input variables are used in the RVP model.

1 Reactor Inlet temperature 0C2 Reactor A outlet temperature 0C3 Reactor B outlet temperature 0C4 Liquid Hourly Space Velocity (LHSV) 1/hr 5 H2 Consumption Sm3/hr6 Deisopentanizer (DIP) tray 8 temperature 0C7 DIP Bottom Flow Rate m3/hr8 DIP Feed Flow Rate9 DIP Reflux Flow Rate10 CP4703 top temperature (Pressure Corrected)11 C-4703 Reflux Flow rate12 C-4703 Feed Flow Rate

The output is RVP measured by laboratory. The data is chosen from a period of approximately9 and 6 months operation for calibration and validation respectively. The total number of inputdata in calibration and validation are 5697, and 3184 respectively. The data corresponding tothe periods of process shutdown and outliers has been omitted. Consequently, there are only233 and 53 laboratory measurements of RVP available for calibration and validation periodsrespectively.

2.2 Model Structure

The structure of the model is based on an ARX model in which the hourly sampled inputvariables are used together with the previous existing output at time t-24 in order to predictthe output at time t. As described in chapter 5, this solution is integrated in the regressionmatrix of the ARX structure, in which the delay time for output is inherently 24 hours.Hence, there will be only one A-parameter, i.e. na=1, and number of B-parameters nb will beas many as it is necessary to get an acceptable low prediction error, compared to the definedreference models described in chapter 5.

In parameter estimation a PLS model is used. A suitable number of principal components orLatent Variable LV need to be found. Number of B-parameters nb and number latent variableLV are determined by a series of recursive simulation of the ARX model, in which minimumof the Root Mean Sum Squares Error in Validation (RMSSEV) is used as the criterion foroptimum number of nb and LV.

Appendix B

198

2.3 Calibration

Another parameter needs to be determined. That is the delay parameters involved with eachinput variables. The delay parameters are also determined by numerous recursive simulations.The following has been found for the input variables.

K = [6 5 10 7 7 5 5 11 15 9 9 16]

Table B.1 shows the values of RMSSV obtained for the different nb and LV, in which themodel order is changed from 1 to 20 in order to search for all possible effect of variables up tot-24, i.e. the previous measured RVP. The maximum number of LV is chosen to be 25 in thiscase.It can be seen that there is only one local minimum that appear already by a second order ARXmodel and LV=4. It can also be seen in figure B.1, which shows a plot of RMSSEV versusboth LV and nb, and in figure B.2, which shows RMSSEV as a function of LV for nb=2.Hence, there is only one solution, and the model structure with nb=2, and LV=4 is chosen.

nb Min. RMSSEV X-Block Y-Block LV

1 1.043 78.56 82.97 4

2 1.036 78.07 82.87 4

3 1.085 78.42 82.84 4

4 1.086 78.68 82.45 4

5 1.099 78.76 82.10 4

6 1.140 78.71 81.87 4

7 1.190 83.88 82.65 5

8 1.201 82.11 82.90 5

9 1.211 81.22 82.96 5

10 1.222 80.95 83.07 5

11 1.225 80.66 82.95 5

12 1.211 79.73 82.79 5

13 1.207 78.50 82.68 5

14 1.215 78.54 82.74 5

15 1.221 78.64 82.71 5

16 1.209 78.70 82.64 5

17 1.200 78.73 82.63 5

18 1.198 78.83 82.51 5

19 1.199 78.83 82.54 5

20 1.218 78.8395 82.606 5

Table B.1 : RVP model, Minimum RMSSEV for different nb, and LV.

Appendix B

199

0 5 10 15 20 250

10

201

1.5

2

2.5RVPLAB, RMSSEV VS nb and LV

LV

nb

RM

SS

EV

Figure B.1 : RVP Model, RMSSEV as a function of nb and LV.

0 5 10 15 20 251

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8


Number of LV

RM

SS

EV

Figure B.2 : RVP Model, RMSSEV as a function of LV for nb =2.

Appendix B

200

The prediction error for this model is shown in figure B.3. Notice that the number of availableRVP measurements are only 233. Figure B.4 shows a histogram plot of prediction error incalibration, which exhibit an approximate zero mean error.

0 50 100 150 200 250-8

-6

-4

-2

0

2

4


Figure B.3 : RVP Model, prediction error in calibration.

-8 -6 -4 -2 0 2 4 60

5

10

15

XBIN

BIN


Figure B.4 : RVP Model, histogram plot of prediction error in calibration

Figure B.5 shows the open-loop simulation of the model by using calibration data set.Open-loop simulation is performed by letting the new predicted value of the output be usedinstead of measurement for prediction of the next output value. Figure B.6 shows the resultfor simulation of the model in which the actual output measurement is used for prediction ofthe next output. As it can be seen from figure B.5 and B.6, the model has captured theessential variation of RVP. Figure B.7 shows measured RVP at laboratory versus modelpredicted RVP in calibration.

Appendix B

201

0 50 100 150 200 25060

62

64

66

68

70

72

74

76


Sample

RV

P S

imul

ated

(o) a

nd R

VP

LA

B(*

)

Figure B.5: RVP Model, open loop simulation in calibration

0 50 100 150 200 25060

62

64

66

68

70

72

74

76

78RVP LAB, Calibration, OR=2 LV=4

Sample

RV

P L

AB

(*) a

nd R

VP

Mod

el(o

)

Figure B.6: RVP Model, prediction ability in calibration

Appendix B

202

60 65 70 75 8060

62

64

66

68

70

72

74

76

78

80RVP LAB, Calibration, OR=2 LV=4

RVP Model

RV

P L

AB

Figure B.7 : Measured RVP vs. model predicted RVP in calibration.

Selection of the best nb and LV is based on performance of the obtained model in validation.The important issue is to capture the maximum effect of input variables on prediction ofoutput and obtain a model with minimum prediction error. The issues in validation of theselected model is discussed in the following subsection.

2.4 Validation

The validation is performed applying a completely distinct set of data. As mentioned beforethe input data in validation set consists of 3184 data set covering 6 months operation. In thisperiod, after omitting the outliers, there are only 53 laboratory measurements of output RVPis remained.





Table B.2: RMSSE, average-model, and zero-model in validation and calibration.

The RMSSE in validation, the average-model RMSEAVGV and the zero-model RMSEZROVare shown in table B.2. It can be seen that the RMSSEV is less than average- and zero-model,indicating that the model has captured the essential variation both in input and output.

The prediction error in validation is shown in figure B.8. Figure B.9 shows a histogram plot ofprediction error in validation.

Appendix B

203

0 10 20 30 40 50 60-3

-2

-1

0

1

2

3


Figure B.8: RVP Model, prediction error in validation.

-3 -2 -1 0 1 2 3 40

1

2

3

4

5

6

XBIN

BIN

Error in Validation

Figure B.9: RVP Model, histogram plot of prediction error in validation.

Appendix B

204

0 10 20 30 40 50 6066

67

68

69

70

71

72

73


Sample

RV

P S

imul

ated

(o) a

nd R

VP

LA

B(*

)

Figure B.10: RVP Model, Open Loop Simulation in validation

Figure B.10 shows the open-loop simulation in the validation, in which the predicted value ofthe output is used to predict the next output value. Open-loop simulation shows thepredictability of the model during a period of operation without having the actual outputmeasurement. Figure B.11 shows the result of the simulation when the actual measurements are used. Theresult in figure B.11 can be better expressed in figure B.12, which shows measured versusmodel predicted RVP in validation.

As we can see the model has captured the essential variation in the data and the predictionability is satisfactory.

Appendix B

205

0 10 20 30 40 50 6066

67

68

69

70

71

72

73

74RVP LAB, Validation, OR=2 LV=4

Sample

RV

P L

AB

(*) a

nd R

VP

Mod

el(o

)

Figure B.11 : RVP Model, prediction ability in calibration

60 65 70 75 8060

62

64

66

68

70

72

74

76

78

80RVP LAB, Validation, OR=2 LV =4

RVP Model

RV

P L

AB

Figure B.12: RVP Model, prediction ability in calibration

Appendix B

206

3 RON Model

3.1 Introduction

In this section the model for prediction of Research Octane Number (RON) for isomerateproduct from isomerization unit will be presented.

3.2 Inputs an Output

The following input variables are used in the RON model.

1 Reactor Inlet temperature 0C2 Reactor A outlet temperature 0C3 Reactor B outlet temperature 0C4 Liquid Hourly Space Velocity (LHSV) 1/hr 5 H2 Consumption Sm3/hr6 Deisopentanizer (DIP) tray 8 temperature 0C7 DIP Bottom Flow Rate m3/hr8 DIP Feed Flow Rate9 DIP Reflux Flow Rate10 CP4703 top temperature (Pressure Corrected)11 C-4703 Reflux Flow rate12 C-4703 Feed Flow Rate

The total number of input data are 5699, and 4266 in calibration and validation data setrespectively. These number of data set corresponds to 9 months operation data in calibrationand 6 months operation data in validation. Notice that the data corresponding to the periods ofprocess shutdown and outliers has been omitted. Regarding the output RON, there are only238 and 100 laboratory measurements available in calibration and validation periodsrespectively.

3.3 Model Structure

Effective feedback control, based on manipulating the temperature of the reactors, has causedsmall variation in the RON quality, as it is shown in table B.3. Notice that this is thecalibration data set that cover 9 months of operation. It has been found that the type of model structure used in the case of RVP model is notsuitable for prediction of RON. As it is shown in chapter 4, there is more variation in the RVP.This is particularly due to the control strategy in this unit, which is based on effective controlof RON quality.

As it is discussed in chapter 5, linear interpolation is performed in order to estimate themissing RON values, which is consequently based on the assumption that the variation ofRON from one day to another is small enough to permit a rough estimation of RON betweentwo subsequent existing RON measurement.

Appendix B

207

Since we are applying interpolation in order to estimate the missing RON output, we will havean equal number of observations in both input and output data set. The number ofA-parameters, and B-parameters are then determined by model order, and we will have thesame number of na, and nb. The model structure is based on an ARX model, in which PLS isused for parameter estimation.

Calibration Temperature

RON Reactor Inlet Reactor A Outlet Reactor B Outlet

Average 87.29 142.96 189.10 159.80

Std. Deviation 0.47 2.21 2.28 2.52

Maximum 88.60 147.30 193.81 164.20

Minimum 85.70 100.27 132.52 112.18

Table B.3 : RON and reactor outlet temperatures in calibration data set.

It is important to emphasize that the interpolation is performed only in calibration data set. Inthe validation, we let the model apply its own predicted output, in order to predict the nextoutput.

3.4 Calibration

Optimum number of model order nb, Latent Variable LV, and a set of suitable delayparameters k has been found by numerous recursive simulations.The following delay parameters has been found for the input variables:

k = [ 5 4 4 7 6 2 3 10 9 9 10 11 ]


Table B.4 shows the values of RMSSV obtained for the different nb and LV, in which themodel order is changed from 1 to 25 and LV is changed from 1 to 25.

It can be seen that there is only one local minimum that appear already by a second order ARXmodel and LV=5. It can also be seen in figure B.13, which shows a plot of RMSSEV versusboth LV and nb, and in figure B.14, which shows RMSSEV as a function of LV for nb=2.

It can be seen that the value of RMSSEV is less in the case of nb=1. However, the case withnb=2 is preferable since the captured variance in both inputs (X-block) and output (Y-block)are higher.

Hence, the model structure with nb=2, and LV=5 is chosen.

Appendix B

208


1 0.239 77.53 67.55 3

2 0.244 83.57 70.52 5

3 0.260 75.56 67.33 3

4 0.269 75.65 66.96 3

5 0.274 75.44 66.55 3

6 0.280 88.96 72.34 7

7 0.287 88.64 73.23 7

8 0.294 87.99 73.77 7

9 0.294 87.24 74.64 7

10 0.295 86.93 74.81 7

11 0.290 86.60 75.31 7

12 0.297 86.27 75.60 7

13 0.303 85.20 75.79 7

14 0.303 83.16 75.64 7

15 0.319 83.07 76.23 7

16 0.310 82.96 76.23 7

17 0.308 82.85 76.27 7

18 0.304 82.82 76.13 7

19 0.308 82.86 75.98 7

20 0.315 82.84 75.96 7

Table B.4 : RON model, min. RMSSEV for different value of ARX order and LV.

0 5 10 15 20 250

10

20

0.2

0.4

0.6

0.8RVPLAB, RMSSEV VS nb and LV

LV

nb

RM

SS

EV

Figure B.13 : RMSSEV as a function of nb and LV.

Appendix B

209

0 5 10 15 20 250.24

0.25

0.26

0.27

0.28

0.29

0.3

0.31


Number of LV

RM

SS

EV

Figure B.14: RON model, RMSSEV as a function of LV for nb=2.

0 50 100 150 200 250-2

-1.5

-1

-0.5

0

0.5

1


Figure B.15: RON model, prediction error in calibration.

Appendix B

210

-2 -1.5 -1 -0.5 0 0.5 1 1.50

5

10

15

20

25

XBIN

BIN


Figure B.16: RON model, histogram plot for prediction error in calibration.

The prediction error for this model is shown in figure B.15. The number of available RONmeasurements are only 238. Figure B.16 shows a histogram plot of prediction error incalibration, which exhibit an approximate zero mean error.

0 50 100 150 200 25085.5

86

86.5

87

87.5

88

88.5

89RON LAB, Calibration, Open Loop Simulation

Sample

RO

N S

imul

ated

(o) a

nd R

ON

LA

B(*

)

Figure B.17: RON model, open loop simulation in calibration.

Appendix B

211

85 85.5 86 86.5 87 87.5 88 88.5 8985

85.5

86

86.5

87

87.5

88

88.5

89RON LAB, Calibration, OR=2 LV =6

RON Model

RO

N L

AB

Figure B.18 Measured versus predicted RON in calibration.

Figure B.17 shows the open-loop simulation of the model by using calibration data set.Open-loop simulation is performed by letting the new predicted value of the output be usedinstead of measurement for prediction of the next output value. Figure B.18 shows measuredversus model predicted RON in calibration.As it can be seen from figure B.17 and B.18, the model has captured the essential variation inthe data.

3.5 Validation

The validation is performed applying a completely distinct set of data. As mentioned beforethe input data in validation set consists of 4266 data set covering 6 months operation. In thisperiod, after omitting the outliers, there are only 100 laboratory measurements of output RONis remained.





Table B.5 : RMSSE, average-model, and zero-model in validation and calibration.

The RMSSE in validation, the average-model RMSEAVGV and the zero-model RMSEZROVare shown in table B.5. It can be seen that the RMSSEV is less than average- and zero-model,indicating that the model has captured the essential variation both in input and output.

Appendix B

212

The prediction error in validation is shown in figure B.19. Figure B.20 shows a histogram plotof prediction error in validation.

0 20 40 60 80 100-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6


Figure B.19: RON model, prediction error in validation.

-1 -0.5 0 0.5 10

1

2

3

4

5

6

7

8

9

XBIN

BIN

Error in Validation

Figure B.20: RON model, histogram plot for prediction error in validation.

Figure B.21 shows the open-loop simulation in the validation, in which the predicted value ofthe output is used to predict the next output value. Open-loop simulation shows thepredictability of the model during a period of operation without having the actual outputmeasurement.

Appendix B

213

0 20 40 60 80 10086.4

86.6

86.8

87

87.2

87.4

87.6

87.8

88

88.2

88.4RON LAB, Validation, Open Loop Simulation

Sample

RO

N S

imu

late

d(o

) an

d R

ON

LA

B(*

)

Figure B.21: RON model, open loop simulation in validation.

85 85.5 86 86.5 87 87.5 88 88.5 8985

85.5

86

86.5

87

87.5

88

88.5

89RON LAB, Validation, OR=2 LV =6

RON Model

RO

N L

AB

Figure B.22: Measured versus predicted RON in validation.

The result in figure B.21 can be better expressed in figure B.22, which shows measured versusmodel predicted RON in validation.As we can see the model has captured the essential variation in the data and the predictionability is satisfactory.

Appendix B

214

Appendix C

Multiple Period BlendingResults

Appendix C

215

1 Product Order Number 1Order Number 1: D92

Final Product Volume RON Benzene RVP

D92 2400 92 1.49 95

Components TimePeriod

Volumem3

MTBE 0 0 0 0 0

Butane 0 237.93 93 0 460

Import 0 0 0 0 0

LVN 0 428.57 72.81 0 77

IC5 0 16 89 0 150

Isomerate (42) 0 280 89 1 70

Isomerate (23) 0 280 89 1 70

Reformate II 0 601.50 100.57 5 35


Reformate I 0 200 100 0 45

LVBN 0 16 86 0 125

Qualities and the volume of the final product and the blend components

Appendix C

216



D95 4800 95 0,61 95


Volumnm3

MTBE 2 0 0 0 0

MTBE 3 0 0 0 0

Butane 2 263,94 93 0 460

Butane 3 239,59 93 0 460

Import 2 0 0 0 0

Import 3 0 0 0 0

LVN 2 240 75 0 77

LVN 3 13,08 75 0 77

IC5 2 32 89 0 150

IC5 3 16 89 0 150

Isomerate (42) 2 453,88 89 1 70

Isomerate (42) 3 228,05 89 1 70

Isomerate (23) 2 0 0 0 0

Isomerate (23) 3 676,04 89 1 70

Reformate II 2 680 101 2.32 35

Reformate II 3 340 101 0 35

Reformate I+II 2 512,3 101 0 35

Reformate I+II 3 457,11 101 0 35

Reformate I 2 217,87 100 0 45

Reformate I 3 382,13 100 0 45

LVBN 2 0 0 0 0

LVBN 3 48 86 0 125

Appendix C

217



D98 2400 98 0,16 95


Volumnm3

MTBE 7 0 0 0 0

Butane 7 306,22 93 0 460

Import 7 0 0 0 0

LVN 7 0 0 0 0

IC5 7 0 0 0 0

Isomerate (42) 7 0 0 0 0

Isomerate (23) 7 395,85 89 1 70


Reformate I+II 7 1697,93 101 0 35

Reformate I 7 0 0 0 0

LVBN 7 0 0 0 0

Appendix C

218

4 Product Order Number 4Order Number 4: S95


S95 5400 95 0 95

Component Time Period Volume (m3)

MTBE 12 0 0 0 0

MTBE 13 0 0 0 0

MTBE 14 0 0 0 0

Butane 12 193,03 93 0 460

Butane 13 175,01 93 0 460

Butane 14 153,87 93 0 460

Import 12 0 0 0 0

Import 13 0 0 0 0

Import 14 0 0 0 0

LVN 12 301,82 75 0 77

LVN 13 11,99 75 0 77

LVN 14 239,48 75 0 77

IC5 12 0 0 0 0

IC5 13 0 0 0 0

IC5 14 176 89 0 150

Isomerate (42) 12 0 0 0 0

Isomerate (42) 13 0 0 0 0

Isomerate (42) 14 0 0 0 0

Isomerate (23) 12 9,38 89 0 70

Isomerate (23) 13 679,57 89 0 70

Isomerate (23) 14 0 0 0 0







Reformate I 12 1295,76 100 0 45

Reformate I 13 933,44 100 0 45

Reformate I 14 1230,65 100 0 45

LVBN 12 0 0 0 0

LVBN 13 0 0 0 0

LVBN 14 0 0 0 0

Appendix C

219

5 Product Order Number 5Order Number 5: S98


S98 3000 98 1,58 95


Volumnm3

MTBE 16 0 0 0 0

MTBE 17 0 0 0 0

Butane 16 191,39 93 0 460

Butane 17 191,39 93 0 460

Import 16 0 0 0 0

Import 17 0 0 0 0

LVN 16 0 0 0 0

LVN 17 0 0 0 0

IC5 16 0 0 0 0

IC5 17 0 0 0 0

Isomerate (42) 16 0 0 0 0

Isomerate (42) 17 0 0 0 0

Isomerate (23) 16 247,41 89 1 70

Isomerate (23) 17 247,41 89 1 70



Reformate I+II 16 1061,2 101 4.01 35

Reformate I+II 17 1061,2 101 0 35



LVBN 16 0 0 0 0

LVBN 17 0 0 0 0

Appendix C

220

6 Product Order Number 6Order Number 6: G91


G91 5400 91 0,25 90


MTBE 18 0 0 0 0

MTBE 19 0 0 0 0

MTBE 20 0 0 0 0

Butane 18 134,13 93 0 460

Butane 19 159,07 93 0 460

Butane 20 134,13 93 0 460

Import 18 0 0 0 0

Import 19 0 0 0 0

Import 20 0 0 0 0

LVN 18 376,7 75 0 77

LVN 19 514,13 75 0 77

LVN 20 376,7 75 0 77

IC5 18 0 0 0 0

IC5 19 0 0 0 0

IC5 20 0 0 0 0

Isomerate (42) 18 0 0 0 0

Isomerate (42) 19 280 89 1 70

Isomerate (42) 20 531,23 89 1 70

Isomerate (23) 18 531,23 89 1 70

Isomerate (23) 19 0 0 0 0

Isomerate (23) 20 0 0 0 0





Reformate I+II 19 846,8 101 0 35


Reformate I 18 757,93 100 0 45


Reformate I 20 757,93 100 0 45

LVBN 18 0 0 0 0

LVBN 19 0 0 0 0

LVBN 20 0 0 0 0

Appendix C

221



D92 2400 92 0,3 95


Volumnm3

MTBE 23 0 0 0 0

Butane 23 215,7 93 0 460

Import 23 0 0 0 0

LVN 23 389,59 75 0 77

IC5 23 0 0 0 0

Isomerate (42) 23 89,57 89 1 70

Isomerate (23) 23 633,82 89 1 70


Reformate I+II 23 6,79 101 0 35

Reformate I 23 1064,54 100 0 45

LVBN 23 0 0 0 0

Appendix C

222

8 Product Order Number 8Order Number 8 : G95


G95 3000 95 0,27 90


Volumnm3

MTBE 24 0 0 0 0

MTBE 25 0 0 0 0

Butane 24 142,28 93 0 460

Butane 25 131,72 93 0 460

Import 24 0 0 0 0

Import 25 0 0 0 0

LVN 24 26,56 75 0 77

LVN 25 23,33 75 0 77

IC5 24 0 0 0 0

IC5 25 51,63 89 0 150

Isomerate (42) 24 348,97 89 0 70

Isomerate (42) 25 560 89 1 70

Isomerate (23) 24 248,63 89 1 70

Isomerate (23) 25 0 0 0 0



Reformate I+II 24 733,56 101 0 35

Reformate I+II 25 733,32 101 0 35



LVBN 24 0 0 0 0

LVBN 25 0 0 0 0

Appendix C

223

9 Product Order Number 9Order Number 9 : D98


D98 2400 98 2 95


Volumnm3

MTBE 28 0 0 0 0

Butane 28 290,65 93 0 460

Import 28 0 0 0 0

LVN 28 0 0 0 0

IC5 28 0 0 0 0

Isomerate (42) 28 332,63 89 1 70

Isomerate (23) 28 0 0 0 0

Reformate II 28 893,47 101 5 35


Reformate I 28 883,25 100 0 45

LVBN 28 0 0 0 0

Appendix C

224


Final product Volume RON Benzene RVP

D95 4800 95 1,18 95


Volumem3

MTBE 32 0 0 0 0

MTBE 33 0 0 0 0

Butane 32 258,18 93 0 460

Butane 33 233,13 93 0 460

Import 32 0 0 0 0

Import 33 0 0 0 0

LVN 32 50,34 75 0 77

LVN 33 26,91 75 0 77

IC5 32 0 0 0 0

IC5 33 115,87 89 0 150

Isomerate (42) 32 156,4 89 1 70

Isomerate (42) 33 870,4 89 1 70

Isomerate (23) 32 762,41 89 0.37 70

Isomerate (23) 33 0 0 0 0


Reformate II 33 1076,71 101 0 35

Reformate I+II 32 1172,67 101 3.72 35

Reformate I+II 33 76,98 101 0 35



LVBN 32 0 0 0 0

LVBN 33 0 0 0 0

Appendix C

225



G91 5400 91 0,21 90


MTBE 36 0 0 0 0

MTBE 37 0 0 0 0

MTBE 38 0 0 0 0

Butane 36 134,13 93 0 460

Butane 37 147,47 93 0 460

Butane 38 147,47 93 0 460

Import 36 0 0 0 0

Import 37 0 0 0 0

Import 38 0 0 0 0

LVN 36 376,7 75 0 77

LVN 37 376,39 75 0 77

LVN 38 376,39 75 0 77

IC5 36 0 0 0 0

IC5 37 0 0 0 0

IC5 38 0 0 0 0

Isomerate (42) 36 0 0 0 0

Isomerate (42) 37 586,17 89 1 70

Isomerate (42) 38 0 0 0 0

Isomerate (23) 36 531,23 89 1 70

Isomerate (23) 37 0 0 0 0

Isomerate (23) 38 586,17 89 0 70


Reformate II 37 689,97 101 0 35

Reformate II 38 689,97 101 0 35




Reformate I 36 757,93 100 0 45



LVBN 36 0 0 0 0

LVBN 37 0 0 0 0

LVBN 38 0 0 0 0

Appendix C

226

12 Product Order Number 12Order Number 12 : S98


S98 3000 98 0,44 95


Volumem3

MTBE 40 0 0 0 0

MTBE 41 0 0 0 0

Butane 40 191,39 93 0 460

Butane 41 191,39 93 0 460

Import 40 0 0 0 0

Import 41 0 0 0 0

LVN 40 0 0 0 0

LVN 41 0 0 0 0

IC5 40 0 0 0 0

IC5 41 0 0 0 0

Isomerate (42) 40 39,45 89 0 70

Isomerate (42) 41 156,4 89 1 70

Isomerate (23) 40 207,96 89 1 70

Isomerate (23) 41 91 89 1 70

Reformate II 40 172,57 101 5 35


Reformate I+II 40 888,63 101 0 35

Reformate I+II 41 1061,2 101 0 35



LVBN 40 0 0 0 0

LVBN 41 0 0 0 0

Appendix C

227

13 Product Order Number 13Order Number 13 : S95


S95 5400 95 1,65 95


MTBE 42 0 0 0 0

MTBE 43 0 0 0 0

MTBE 44 0 0 0 0

Butane 42 174,05 93 0 460

Butane 43 191,43 93 0 460

Butane 44 191,43 93 0 460

Import 42 0 0 0 0

Import 43 0 0 0 0

Import 44 0 0 0 0

LVN 42 28,47 75 0 77

LVN 43 11,61 75 0 77

LVN 44 11,61 75 0 77

IC5 42 0 0 0 0

IC5 43 0 0 0 0

IC5 44 0 0 0 0

Isomerate (42) 42 280 89 1 70

Isomerate (42) 43 747,22 89 1 70

Isomerate (42) 44 747,22 89 1 70

Isomerate (23) 42 341,88 89 1 70

Isomerate (23) 43 0 0 0 0

Isomerate (23) 44 0 0 0 0


Reformate II 43 849,74 101 5 35

Reformate II 44 513,52 101 5 35



Reformate I+II 44 336,21 101 0 35

Reformate I 42 959,23 100 0 45



LVBN 42 16,37 86 0 125

LVBN 43 0 0 0 0

LVBN 44 0 0 0 0

Appendix C

228



D98 2400 98 2 95


Volumnm3

MTBE 47 0 0 0 0

Butane 47 306,22 93 0 460

Import 47 0 0 0 0

LVN 47 0 0 0 0

IC5 47 0 0 0 0

Isomerate (42) 47 0 0 0 0

Isomerate (23) 47 395,85 89 0 70

Reformate II 47 1697,93 101 2.83 35



LVBN 47 0 0 0 0

Appendix C

229



D95 5400 95 2 95


MTBE 48 0 0 0 0

MTBE 49 0 0 0 0

MTBE 50 0 0 0 0

Butane 48 185,2 93 0 460

Butane 49 191,43 93 0 460

Butane 50 182,12 93 0 460

Import 48 0 0 0 0

Import 49 0 0 0 0

Import 50 0 0 0 0

LVN 48 0 0 0 0

LVN 49 11,61 75 0 77

LVN 50 110,77 75 0 77

IC5 48 0 0 0 0

IC5 49 0 0 0 0

IC5 50 32 89 0 150

Isomerate (42) 48 719,49 89 0.57 70

Isomerate (42) 49 747,22 89 0 70

Isomerate (42) 50 453,2 89 0 70

Isomerate (23) 48 0 0 0 0

Isomerate (23) 49 0 0 0 0

Isomerate (23) 50 0 0 0 0


Reformate II 49 849,74 101 4.24 35


Reformate I+II 48 849,67 101 3.76 35


Reformate I+II 50 381,35 101 5 35



Reformate I 50 640,56 100 2.64 45

LVBN 48 45,63 86 0 125

LVBN 49 0 0 0 0

LVBN 50 0 0 0 0

Appendix C

230



D98 2400 98 2 95


Volumnm3

MTBE 52 0 0 0 0

Butane 52 246,6 93 0 460

Import 52 0 0 0 0

LVN 52 0 0 0 0

IC5 52 80 89 0 150

Isomerate (42) 52 58,8 89 1 70

Isomerate (23) 52 0 0 0 0


Reformate I+II 52 245,01 101 0 35

Reformate I 52 1641,59 100 2.89 45

LVBN 52 128 86 0 125

Appendix C

231



G95 4800 95 1,14 90


MTBE 57 0 0 0 0

MTBE 58 0 0 0 0

MTBE 59 0 0 0 0

Butane 57 133,2 93 0 460

Butane 58 138,04 93 0 460

Butane 59 139,11 93 0 460

Import 57 0 0 0 0

Import 58 0 0 0 0

Import 59 0 0 0 0

LVN 57 76,61 75 0 77

LVN 58 51,32 75 0 77

LVN 59 120 75 0 77

IC5 57 32 89 0 150

IC5 58 0 0 0 0

IC5 59 16 89 0 150

Isomerate (42) 57 280 89 1 70

Isomerate (42) 58 366,38 89 1 70

Isomerate (42) 59 193,62 89 1 70

Isomerate (23) 57 156,4 89 0 70

Isomerate (23) 58 156,4 89 0 70

Isomerate (23) 59 156,4 89 0 70







Reformate I 57 921,79 100 5 45

Reformate I 58 887,85 100 0 45

Reformate I 59 974,87 100 0 45

LVBN 57 0 0 0 0

LVBN 58 0 0 0 0

LVBN 59 0 0 0 0

Appendix C

232

data-based dynamic modeling for refinery optimization · networks (anns) exhibit a strong ability...

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